In [2]:

```
import math
#Initilization of Variables
M=150 #kg #Mass of the Body
a=3 #m/s**2 #Acceleration
#Calculation
#Force
F=M*a #N
#Result
print"FOrce is",round(F,2),"N"
```

In [3]:

```
import math
#Initilization of Variables
F=100 #N #Force
m=4 #kg #mass
t=10 #seconds #time
u=5 #m/s #Initial Velocity
#Calculation
#Acceleration
a=F*m**-1 #m/s**2
#Distance
s=u*t+a*t**2*2**-1 #m
#Result
print"Acceleration is",round(a,2),"m/s**2"
print"Distance moved is",round(s,2),"m"
```

In [4]:

```
import math
#Initilization of Variables
W=980 #N #Weight of body on the earth
g=9.80 #m/s**2 #Acceleration due to gravity
g2=1.6 #m/s**2 #Acceleration due to gravity on moon
g3=270 #m/s**2 #Acceleration due to gravity on sun
#Calculation
#Mass
m=W*g**-1 #Kg
#Weight of body on moon
W1=m*g2 #N
#Weight of body on sun
W2=m*g3 #N
#Result
print"Weight of body on moon",round(W1,2),"N"
print"Weight of body on sun",round(W2,2),"N"
```

In [5]:

```
import math
#Initilization of Variables
F=200 #N #Force
m=300 #kg #mass
t=90 #sec #time
u=20 #m/s #Initial velocity
#Calculation
#Acceleration
a=F*m**-1 #m/s**2
#Final Velocity in Direction of motion
v=u+a*t #m/s
#Final Velocity in opposite direction of motion
v2=u-a*t #m/s
#Result
print"Final Velocity in Direction of motion",round(v,2),"m/s"
print"Final Velocity in opposite direction of motion",round(v2,2),"m/s"
```

In [7]:

```
import math
#Initilization of Variables
m=15 #kg #Mass
h=19.6 #m #Height of body from ground
F=4900 #N #Force of resistance
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#Final Velocity of body
v=(2*g*h)**0.5 #m/s
#Weight of body
W=m*g #N
#Net Force acting in the upward direction
F2=F-W #N
#Acceleration
a=F2*m**-1 #m/s**2
#Part-2
v2=0 #Final Velocity after penetration into the ground
u=v #Initial Velocity on the ground
#Distance penetrated into the ground
s=-(v2**2-u**2)*(2*a)**-1 #m
#Result
print"Distance penetrated into the ground",round(s,3),"m"
```

In [8]:

```
import math
#Initilization of Variables
W=637 #N #Weight of man
h=19.6 #m #Height of Tower
u=0 #m/s #Initial Velocity of man when he reaches the water surface
g=9.8 #m/s**2 #acceleration due to gravity
s=2 #m #Distance travelled
#Calculation
#Final Velocity of man when he reaches the water surface
v=(2*g*h)**0.5 #m/s
#acceleration
a=v**2*(2*s)**-1 #m/s**2 #m/s**2
#Mass of man
m=W*g**-1 #Kg
#Average resistance of water
F=m*a+W #N
#Result
print"Average Resistance of water",round(F,2),"N"
```

In [9]:

```
import math
#Initilization of Variables
m=0.081 #kg
v=300 #m/s #velocity
s=0.1 #m #Depth
s2=0.05 #m #Distance travelled
#Calculation
#Acceleration
a=v**2*(2*s)**-1 #m/s**2
#Force offered by wood to the bullet
F=m*a #N
#Velocity
v=-(u**2-(2*a*s2)) #m/s
v2=v**0.5 #m/s
#Result
print"Force of resistance",round(v2,2),"m/s"
```

In [1]:

```
import math
#Initilization of Variables
v=0 #Final Velocity
s=60 #m #Distance travelled
mu=0.4 #coefficient of friction
g=9.80
#Calculation
#acceleration
a=mu*g #m/s**2
#speed of car
u=(2*a*s)**0.5*1000**-1*3600 #m/s
#Result
print"Speed of car is",round(u,2),"Km/hr"
```

In [11]:

```
import math
#Initilization of Variables
F1=2000 #N #Tractive of force exerted by railway car
W=50 #KN #Weight of car
g=9.81 #m/s**2 #acceleration due to gravity
#Calculation
#mass of car
m=W*1000*g**-1 #N
#Frictional resistance
F2=5*W
#Net Force in Direction of motion
F=F1-F2 #N
#Acceleration
a=F*m**-1
#Result
print"acceleration when the car is moving",round(a,2),"m/s**2"
```

In [12]:

```
import math
#Initilization of Variables
W=1960*1000 #N #Weight of train
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#mass of train
m=W*g**-1 #kg
#final Velocity
v=100*3**-1 #m/s
t=5*60 #sec
#Acceleration
a=v*t**-1 #m/s**2
#Average pull required
F2=m*a+19600
#Result
print"Average pull required",round(F2,2),"N"
```

In [2]:

```
import math
from math import sin, cos, radians, pi
import numpy as np
#Initilization of Variables
W=200 #N #Weight of Body
g=9.81 #m/s**2 #aceleration due to gravity
theta=45 #Degrees #Angle of plane
u=0 #m/s #Initial Velocity
v=2 #m/s #Final velocity
mu=0.1 #coefficient of friction
#Calculation
#Acceleration of body
a=g*(sin(theta*pi*180**-1)-mu*cos(theta*pi*180**-1)) #m/s**2
#Distance
s=(v**2-u**2)*(2*a)**-1 #m
#Result
print"Distance along inclined plane is",round(s,2),"m"
```

In [3]:

```
import math
from math import sin, cos, radians, pi
import numpy as np
#Initilization of Variables
u=0 #m/s #Initial Velocity
theta=20 #degree #Angle of inclination
mu1=0.08 #Coefficient of friction between the plane and lower body
mu2=0.08 #Coefficient of friction between the plane and upper body
d=10 #m #distance beween two body
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Acceleration of lower body down the plane
a1=g*(sin(theta*pi*180**-1)-mu1*cos(theta*pi*180**-1)) #m/s**2
#Acceleration of upper body
a2=g*(sin(theta*pi*180**-1)-mu2*cos(theta*pi*180**-1)) #m/s**2
#Distance travelled by lower body
#s1=u*t+a1*t**2*2**-1
#After sub values and further simplifying we get
#s1=1.3805*t**2 ...................1
#Distance travelled by upper body
#s1=u*t+a1*t**2*2**-1
#After sub values and further simplifying we get
#s1=1.447*t**2 .......................2
#Further simplfying we get
t=(10*0.1385**-1)**0.5 #s
#sub value of t in equation 1 and 2
s1=1.3805*round(t,2)**2 #m
s2=1.447*round(t,2)**2 #m
#Result
print"distance through which each body travels before they meet:s1",round(s1,2),"m"
print" :s2",round(s2,2),"m"
#Answer of s1 is incorrect in book
```

In [15]:

```
import math
from math import sin, cos, radians, pi
import numpy as np
#Initilization of Variables
W=6000 #N #Weight of truck
u=10 #m/s #speed of truck
#sin(theta)=1*40**-1
#Calculation
#Road Resistance
F1=W*1*40**-1 #N
#Frictional Force
F2=F1*(W*10**-3)**-1
#PArt-2
#Speed of truck
u2=2*u #m/s
#Force exerted by engine up theplane
P=W*1*40**-1+F1 #N
#Power Exerted by engine
P2=P*u2*1000**-1 #KW
#Result
print"Frictional Force of truck is",round(F2,2),"N"
print"Power Exerted by engine is",round(P2,2),"KW"
```

In [16]:

```
import math
#Initilization of Variables
W=200*10**3 #N #Weight of train
#sin(theta)=1*150**-1 #Slope of track
u=5 #m/s #speed of train
p=3.5 #KW #Power developed by engine
#Calculation
#Case-1
#power developed by engine
P=p*1000*u**-1 #N
#Net Force
F=W*1*150**-1+P #N
#Case-2
#Force exerted by engine while moving up
P2=W*1*150**-1+F #N
#Power developed by engine
P3=P2*u*1000**-1 #KW
#Result
print"Power Developed by Engine to pull up the train is",round(P3,2),"KW"
#Answer of Power developed by engine is incorrect i.e P so answer of Power Developed by Engine to pull up the train is also incorrect i.e P3
```

In [17]:

```
import math
#Initilization of Variables
L_BC=100 #m #Distance
V=20*3**-1 #m/s #Velocity
W=20000 #N #Weight
g=9.81 #m/s**2 #acceleration due to gravity
m=W*g**-1 #Mass of car
#sin(theta)=5*100**-1
#Calculation
#Frictional resistance due to track
F=8*20 #N
#Final Velocity of car at D
v=0
#Component of weight of train
W2=W*5*100**-1 #N
#Total Retarding Force against motion
F2=F+W2 #N
#acceleration
a=F2*g*W**-1 #m/s**2
#Distance
s=V**2*(2*round(a,3))**-1 #m
#PArt-2
#Dstance travelled by car From B to E
#Distance BD
s_BD=s+L_BC #m
F3=840 #N #Net Force down the grade
#Acceleration
a2=F3*g*W**-1 #m/s**2
#Velocity
v2=(2*a2*s_BD)**0.5 #m/s
#PArt 3
#Motion From B to E
#acceleration
a3=F*g*W**-1 #m/s**2
#Initial velocity at B
u_B=10.70 #m/s
#Distance
s2=u_B**2*(2*round(a3,3))**-1 #m
#Result
print"Distance travelled by car before stopping is",round(s,2),"m"
print"Distance travelled by car beyond Bon level track before stopping at E",round(s2,2),"m"
```

In [18]:

```
import math
#Initilization of Variables
W=100 #N #Weight carried by lift
a=2.45 #m/s**2 #Acceleration
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#Tension in the cables supporting the lift
#Lift moving upwards
T=W*(1+a*g**-1) #N
#Lift moving downwards
T2=W*(1-a*g**-1) #N
#Result
print"Tension in the cables supporting the lift:when moving upwards",round(T,2),"N"
print"Tension in the cables supporting the lift:when moving downward",round(T2,2),"N"
```

In [19]:

```
import math
#Initilization of Variables
a=1 #m/s**2 #upward acceleration
W=600 #N #weight of man
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#NEt Force in upward direction
F=W*g**-1 #N
#But net Force in upward direction
T=F+W #N
#Result
print"net Force in upward direction",round(T,2),"N"
```

In [20]:

```
import math
#Initilization of Variables
a=1.225 #m/s**2 #upward acceleration
W=500 #N #Weight of man
g=9.8 #m/s**2 #Acceleration due to gravity
#Calculation
#Tension in the cables supporting the lift
#Lift moving upwards
T=W*(1+a*g**-1) #N
#lift moving downwards
T2=W*(1-a*g**-1) #N
#Lift moving upwards with unknown acceleration
T3=600 #N #Pressure exerted by man
a=(T3-W)*g*W**-1 #m/s**2
#Result
print"Acceleration upwards is",round(a,2),"m/s**2"
```

In [21]:

```
import math
#Initilization of Variables
W=2500 #N #Weight of an elevator
u=0 #m/s #Initial Velocity
s=35 #m #Distance travelled
t=10 #sec #time
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Tension in the cables
#When acceleration is zero i.e a=0
a=0 #m/s**2
T=W*(1-a*g**-1) #N
#When acceleration is zero i.e a=0
a2=9.81 #m/s**2
T2=W*(1-a2*g**-1) #N
#Using equation of distance
a3=(s-u*t)*2*(t**2)**-1 #m/s**2
#Tension in the cable at time t=10 sec
T3=W*(1-a3*g**-1) #N
#Result
print"Limits of table Tension is:when a=0",round(T,2),"N"
print" :when a=9.81 m/s**2",round(T2,2),"N"
print"Cable Tension at time t=10 sec",round(T3,2),"N"
```

In [22]:

```
import math
#Initilization of Variables
g=9.80 #m/s**2 #Acceleration due to gravity
W=5000 #N #Weight of 10 men on the cage
u=0 #m/s #Initial Velocity of cage
v=12 #m/s #Final Velocity
s=20 #m #Distance travelled
#Calculation
#acceleration
a=(v**2-u**2)*(2*s)**-1 #m/s**2
#Tension in cable while moving downwards
T=W*(1-a*g**-1) #N
#Tension produced by one men
T2=T*10**-1 #N
#Result
print"Pressure Exerted by each man on the cage",round(T2,2),"N"
```

In [4]:

```
import math
#Initilization of Variables
W=5000 #N #Weight of elevator
a=3 #m/s**2 #Acceleration
W2=700 #N #weight of perator
g=9.80
#Calculation
#Reaction offered by floor on operator
R=W*g**-1*a+W2 #N
#Total Weight
W3=W+W2 #N
#Total Tension in the cable
T=W3*g**-1*a+W3 #N
#Result
print"Total tension in the cable",round(T,2),"N"
```

In [24]:

```
import math
#Initilization of Variables
W1=50 #N #Heavier Weight
W2=30 #N #lighter Weight
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#Acceleration of the system
a=g*(W1-W2)*(W1+W2)**-1 #m/s**2
#Tension in the string
T=2*W1*W2*(W1+W2)**-1 #N
#Result
print"Acceleration of the system",round(a,2),"m/s**2"
print"Tension in the string",round(T,2),"N"
```

In [25]:

```
import math
#Initilization of Variables
g=9.80 #m/s**2 #Acceleration due to gravity
W1=60 #N #bigger weight
a=3 #m/s**2 #Acceleration of the system
#Calculation
#smaller Weight
W2=-(a*W1*g**-1-W1)*(a*g**-1+1)**-1 #N
#Tension in the string
T=2*W1*W2*(W1+W2)**-1 #N
#Result
print"Smaller Weight is",round(W2,2),"N"
print"Tension in the string",round(T,2),"N"
```

In [26]:

```
import math
#Initilization of Variables
W1=700 #N #Bigger Load
W2=500 #N #Smaller Load
#Calculation
#Weight of block A when acceleration is g/3
W1_1=((3*W2)+W2)*2**-1 #N
#Weight added
W=W1_1-W1 #N
#Result
print"Weight added is",round(W,2),"N"
```

In [27]:

```
import math
#Initilization of Variables
W_A=150 #N #Weight of block A
W_B=50 #N #Weight of block B
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Acceleration
a=(W_A-W_B*2)*((W_B*2+(W_A*2**-1))*g**-1)**-1 #m/s**2
#Acceleration of block B
a_B=a #m/s**2
#Acceleration of block A
a_A=a*2**-1 #m/s**2
#Tensions in the string
T=W_B+W_B*g**-1*a #N
#Result
print"Tensions in the string is",round(T,2),"N"
print"Acceleration of block B is",round(a_B,2),"m/s**2"
print"Acceleration of block A is",round(a_A,2),"m/s**2"
```

In [28]:

```
import math
#Initilization of Variables
W1=15 #N #weight over pulley A
W2=10 #N #total weight over pulley B
w1=6 #N #weight over pulley B
w2=4 #N #weight over pulley B
g=9.80 #m/s**2 #acceleration due to gravity
#Calculation
#Consider motion of weight 15 N
#(W1-T1)=W1*g**-1*a ..........................(1)
#Consider motion of weight 4 N
#(T2-w2)=w2*g**-1*(a1+a) ...................(2)
#Consider motion of weight 6 N
#(w1-w2)=w1*g**-1*(a1-a) .........................(3)
#Consider motion of pulley B
#T1=2*T2 ...............................(4)
#Adding equations 2 and 3 we get
#g=5*a1-a .......................................(5)
#Multiplying equation (2) by 2
#2*T2-8=8*g**-1*(a1+a)
#But sub value 2*T2=T1 in equation above
#T1-8=8*g**-1*(a1+a) .......................................(6)
#Adding equation 1 and 6
#7*g=23*a+8*a1 .......................................(7)
#Multiplying equation (5) by 23
#23*g=-23*a+5*23*a1 .......................................(8)
#Adding equation 7 and 8 we get
a1=30*g*123**-1 #m/s**2
#sub value of equation 5 we get
a=5*a1-g #m/s**2
#Acceleration of weight 15 N
a_15=a #m/s**2
#Acceleration of weight 6 N
a_6=a1-a #m/s**2
#Acceleration of weight 4 N
a_4=a1+a #m/s**2
#Result
print"Acceleration of weight 15 N",round(a_15,2),"m/s**2"
print"Acceleration of weight 6 N",round(a_6,2),"m/s**2"
print"Acceleration of weight 4 N",round(a_4,2),"m/s**2"
```

In [29]:

```
import math
#Initilization of Variables
#Weight of bodies
W1=10 #N #Weight placed on Horizontal surface
W2=20 #N #Weight hanging free in air
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Acceleration of the system
a=g*W1*(W1+W2)**-1 #m/s**2
#tension in the string
T=W1*W2*(W1+W2)**-1 #N
#Result
print"Acceleration of the system",round(a,2),"m/s**2"
print"Tension in the string",round(T,2),"N"
```

In [1]:

```
import math
#Initilization of Variables
W1=10 #N #Weight on horizontal surface
mu=0.3 #coefficient of friction
W2=20 #N #Weight hanging free in air
g=9.80
#Calculation
#Acceleration of the system
a=g*(W1-mu*W2)*(W1+W2)**-1 #m/s**2
#tension in the string
T=W1*W2*(1+mu)*(W1+W2)**-1 #N
#Result
print"Acceleration of the system",round(a,2),"m/s**2"
print"Tension in the string",round(T,2),"N"
```

In [2]:

```
import math
#Initilization of Variables
W1=10 #N #Weight of block A
W2=20 #N #weight of block B
mu=0.25 #coefficient of friction
s=2 #m #Distance moved by block
u=0 #Initial velocity of block B
g=9.80
#Calculation
#Acceleration
a=g*(W1-mu*W2)*(W1+W2)**-1 #m/s**2
#velocity of block B
v=u**2+2*a*s #m/s
#Result
print"velocity of block B",round(v,2),"m/s"
```

In [3]:

```
import math
#Initilization of Variables
W2=10 #Weight placed on rough horizontal surface
W1_1=1.5 #N #Weight hanging free in air
W1=0.5 #N #additional weight added
T=1.5 #N #Tension in the string
R=10 #N #Normal Reaction
g=9.80
#Calculation
#Total Weight hanging in air
W=W1_1+W1
#Max Frictional Force
F=T=1.5 #N
#Coefficient of friction
mu=F*R**-1
#Acceleration of two weights
a=g*(W-mu*W2)*(W+W2)**-1 #m/s**2
#Tension in the string
T1=W*W2*(1+mu)*(W+W2)**-1 #N
#Result
print"Acceleration of two weights is",round(a,3),"m/s**2"
print"Tension in the string",round(T1,3),"N"
```

In [4]:

```
import math
#Initilization of Variables
W2=1500 #N #weight of body A
W1=1000 #N #Weight of body B
g=9.80
#Coefficient of friction
mu=mu1=mu2=0.2
#T1=1.3691*T2
#Calculation
#Acceleration
a=(W1-1.3691*mu*W2)*((W1*g**-1)+1.3691*W2*g**-1)**-1 #m/s**2
#Tension in the string to which weight 1500 N is attached
T2=W2*g**-1*round(a,2)+mu*W2 #N
#Tension in the string to which weight 1000 N is attached
T1=1.3691*round(T2,3)
#Result
print"Acceleration of the systems is",round(a,2),"m/s**2"
print"Tension in the string:T1",round(T1,2),"N"
print" :T2",round(T2,2),"N"
#Answer for T2 is incorrect in the book
```

In [5]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W1=15 #N #Weight of hanging free in air
W2=40 #N #weight placed on inclined plane
theta=15 #degree #Inclination
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#Acceleration
a=g*(W1-W2*sin(theta*pi*180**-1))*(W1+W2)**-1 #m/s**2
#Tension in string
T=W1*W2*(1+sin(theta*pi*180**-1))*(W1+W2)**-1 #N
#Result
print"Acceleration is",round(a,2),"m/s**2"
print"Tension in the string is",round(T,2),"N"
```

In [6]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W1=25 #N #Weight of hanging free in air
W2=40 #N #weight placed on inclined plane
theta=15 #degree #Inclination
g=9.80 #m/s**2 #Acceleration due to gravity
mu=0.2 #coefficient of friction
#Calculation
#Acceleration
a=g*(W1-W2*sin(theta*pi*180**-1)-mu*W2*cos(theta*pi*180**-1))*(W1+W2)**-1 #m/s**2
#Tension
T=W1*W2*(1+sin(theta*pi*180**-1)+mu*cos(theta*pi*180**-1))*(W1+W2)**-1
#Distance
u=0 #m/s
t=3 #sec
s=u*t+a*t**2*2**-1 #m
#Result
print"Acceleration is",round(a,2),"m/s**2"
print"Tension is",round(T,2),"N"
print"Distance moved by 25 N is",round(s,2),"m"
```

In [36]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
#For Circular Lamina
D=60 #cm
m=0.001 #kg/cm**2 #mass per unit area
#For circular cyclinder
D2=80 #cm
h=15 #cm #height
m2=0.002 #kg/cm**3
#For solid sphere
D3=40 #cm
m3=0.0015 #kg/cm**3
#Calculation
#For Circular Lamina
#Radius
R=D*2**-1 #cm
#Total Mass
M=m*pi*R**2 #kg
#Moment of Inertia of circular section
I_zz=M*R**2*2**-1 #Kg/cm**2
#Radius of Gyration For circular section
k=R*((2)**0.5)**-1 #cm
#For circular cyclinder
#Radius
R2=D2*2**-1 #cm
#Total Mass
M2=m2*pi*R2**2*h #kg
#Moment of Inertia of circular section
I_zz2=M2*R2**2*2**-1 #Kg/cm**2
#Radius of Gyration For circular section
k2=R2*((2)**0.5)**-1 #cm
#For solid sphere
#Radius
R3=D3*2**-1 #cm
#Total Mass
M3=m3*4*pi*R3**3*3**-1 #kg
#Moment of Inertia of circular section
I_zz3=2*5**-1*M3*R3**2 #Kg/cm**2
#Radius of Gyration For circular section
k3=R3*0.6324 #cm
#Result
print"M.I of Circular Lamina is",round(I_zz,2),"Kg/cm**2"
print"Radius of gyration of Circular Lamina is",round(k,2),"cm"
print"M.I of circular cyclinder is",round(I_zz2,2),"Kg/cm**2"
print"Radius of gyration of circular cyclinder is",round(k2,2),"cm"
print"M.I of solid sphere is",round(I_zz3,2),"Kg/cm**2"
print"Radius of gyration of solid sphere is",round(k3,2),"cm"
```

In [7]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
D=90 #cm #Diameter of grindstone
t=10 #cm #Thickness
m=0.0026 #kg/cm**3 #Mass per unit volume
#Calculation
#Radius
R=D*2**-1 #cm
#Total Mass
M=m*pi*R**2*t #kg
#M.I of of grindstone
I_zz=M*R**2*2**-1 #Kg/cm**2
#Radius of gyration
k=R*((2)**0.5)**-1 #cm
#Result
print"M.I of Grindstone is",round(I_zz,2),"Kg/cm**2"
print"Radius of gyration is",round(k,2),"cm"
```

In [38]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
W=1000 #N #Weight of flying wheel
k=0.5 #m
T=1200 #N*m #Torque
g=9.80 #m/s**2
#Calculation
#MAss of flywheel
M=W*g**-1 #Kg
#Moment of Inertia
I=M*k**2 #Kg/m**2
#Angular Acceleration
alpha=T*I**-1 #radians/s**2
#Result
print"Angular Acceleration of flywheel is",round(alpha,2),"radians/s**2"
```

In [39]:

```
import math
#Initilization of Variables
I=12 #Kg*m**2 #M.I of circular disc
t=3 #s #Time
T=800 #N*m #Torque
w_o=0 #m/s #Angular velocity initially
#Calculation
alpha=T*I**-1 #radians/s**2
#Angular velocity after 3 seconds
w=w_o+alpha*t #rad/s
#Result
print"angular Velocity after 3 seconds",round(w,2),"rad/s"
```

In [8]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
M=5000 #kg #Mass of flywheel
k=1 #m #radius of gyration
N_o=400 #r.p.m #Initial Velocity
N=280 #r.p.m #Final speed
t=120 #seconds #Time
#Calculation
#Initial Angular velocity
w_o=2*pi*N_o*60**-1 #rad/s
#Final Angular velocity
w=2*pi*N*60**-1 #rad/s
#M.I
I=M*k**2 #kg/m**2
#Angular acceleration
alpha=(w-w_o)*t**-1 #rad/s**2
#Torque
T=-M*alpha #N*m
#Final K.E
E2=round(w,2)**2*I*2**-1 #N*m
#Initial K.E
E1=41.88**2*I*2**-1 #N*m
#Change in K.E
E=E2-E1 #N*m
#Initial Momentum
p1=I*round(w,2) #N*m/s
#Final Momentum
p2=I*41.88 #N*m/s
#Change in angular Momentum
p=p2-p1 #N*m/s
#Result
print p1
print"Retading Torque acting is",round(T,2),"N*m"
print"Change in K.E is",round(E,2),"N*m"
print"Change in Angular Momentum is",round(p,2),"N*m/s"
```

In [41]:

```
import math
#Initilization of Variables
V=0.2 #m/s #Linear Velocity
W=0.1 #N #Weight of cyclinder
R=0.1 #m #Radius
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Mass
M=W*g**-1 #Mass
#M.I
I=M*R**2*2**-1
#Angular Velocity
w=V*R**-1 #rad/s
#Total K.E
E=(I*w**2+M*V**2)*2**-1 #N*m
#Result
print"Total Kinetic Energy is",round(E,6),"N*m"
```

In [9]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
k=0.5 #m #Radius of Gyration
W=6000 #N #Weight of flywheel
N_o=0 #Initial r.p.m
N=200 #Final r.p.m
t=120 #seconds
g=9.80 #m/s**2
#Calculation
#MAss
M=W*g**-1 #Kg
#Initial Angular Velocity
w_o=2*pi*N_o*60**-1
#Final Angular Velocity
w=2*pi*N*60**-1 #rad/s
#M.I
I=M*k**2
#Angular acceleration
alpha=(w-w_o)*t**-1 #rad/s**2
#Torque Exerted
T=I*alpha #N*m
#Result
print"Average Torque exerted is",round(T,2),"N*m"
#Answer for M.I is incorrect so value of Torque in book is incorrect
```

In [10]:

```
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
#weights
W_A=100 #N
W_B=180 #N
#Radii
r_A=0.1 #m
r_B=0.15 #m
#RAdius of gyration
k_A=0.08 #m
k_B=0.13 #m
theta=30 #degree #Inclination of plane
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Wheel A
#Angular acceleration
alpha_A=(W_A*sin(theta*pi*180**-1)*r_A)*(W_A*g**-1*(k_A**2+r_A**2))**-1 #rad/s
#Linear acc. of wheel
alpha_A_a=alpha_A*r_A #m/s**2
#Wheel B
#Angular acceleration
alpha_B=W_B*sin(theta*pi*180**-1)*r_B*((W_B*g**-1*(k_B**2+r_B**2)))**-1
#Linear acc. of wheel
alpha_B_b=alpha_B*r_B #m/s**2
#Acceleration of A with respect to B
a_A_B=-(round(alpha_B_b,2)-round(alpha_A_a,2))
#Result
print"Acceleration of A with respect to B",a_A_B,"m/s**2"
```

In [44]:

```
import math
#Initilization of Variables
W=5 #N #Weight suspended by arope
W_o=50 #N #Weight of pulley
R=0.3 #m #Radius of pulley
g=9.81 #m/s**2
#Calculation
#Acceleration
a=g*W*(W+W_o*2**-1)**-1 #m/s**2
#Tension in the string
T=W*W_o*(2*W+W_o)**-1 #N
#Result
print"Acceleration is",round(a,2),"m/s**2"
print"Tension in the string is",round(T,2),"N"
```

In [11]:

```
import math
#Initilization of Variables
W1=100 #N #bigger Weight
W2=40 #N #Smaller Weight
W_o=50 #N #Weight of pulley
g=9.80
#Calculation
#Acceleration
a=g*(W1-W2)*(W1+W2+W_o*2**-1)**-1 #m/s**2
#TEnsion T1
T1=W1*(2*W2+W_o*2**-1)*(W1+W2+W_o*2**-1)**-1 #N
#Tension T2
T2=W2*(2*W1+W_o*2**-1)*(W1+W2+W_o*2**-1)**-1 #N
#Result
print"Acceleration of block is",round(a,2),"m/s**2"
print"Tension T1",round(T1,2),"N"
print"Tension T2",round(T2,2),"N"
```

In [46]:

```
import math
#Initilization of Variables
W=2940 #N #Weight of cage
D=1.20 #m #Diameter of drum
R=0.6 #m #Radius of drum
W_o=735 #N #Weight of drum
k=0.55 #m #Radius of gyration
T1=4000 #N*m #Constant Torque Exerted by motor
g=9.8 #m/s**2 #Acceleration due to gravity
#Calculation
#Mass of the cage
M=W*g**-1 #Kg
#Net Force
#(P-W)=M*a ........................1
#M.I of Drum
I=W_o*g**-1*k**2
#Torque on Drum
#(T1-R*P)=I*alpha ..................(2)
#Angular Acceleration
#alpha=(a*R**-1)
#Sub value of I and alpha in equation 2 we get
#(4000-0.6*P)=37.8125*a ...................3
#After multipliying equation 1 by R we get
#(R*P-R*W)=R*M*a .............................4
#Adding equations 3 and 4 we get equation as
#(4000-0.6*2940)=37.8125*a+0.6*300*a
#AFter further simplifying we get
a=2236*(217.8125)**-1 #m/s**2 #Acceleration
#Sub value of a in equation 1
P=M*a+W #N
#PArt-2
#Time Required to raise the cage 20 m from ground
u=0 #m/s #Initial Velocity
a=10.265 #m/s**2 #acceleraation
s=20 #m #Height from ground
#time required
t=((2*s)*a**-1)**0.5 #s
#Result
print"Acceleration of the cage is",round(a,2),"m/s**2"
print"Tension in the cage is",round(P,2),"N"
print"Time required to raise the cage 20 m from ground",round(t,2),"s"
```

In [47]:

```
import math
#Initilization of Variables
W_o=100 #N #Weight of cyclinder
W=10 #N #Weight of block
D=1 #m #diameter of cyclinder
R=0.5 #m #Radius of cyclinder
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#Mass of block
M=W*g**-1 #Kg
#Net Force
#(W-P)=W1*g**-1*alpha .........................1
#M.I
I=M*R**2*2**-1 #kgm**2
#Torque equation
#T=I*alpha
#Multiplying equation of net force with 2 we get
#P=25*g**-1*alpha ..............................2
#Adding equations 1 and 2 we get
alpha=W*3.06**-1 #rad/s**2
#Initial velocity
u=0 #m/s
t=2 #sec #time
#Angular acceleration
alpha=3.268 #rad/s**2
#Angular Velocity
u_o=u+alpha*t
#Result
print"Angular Velocity after 2 seconds is",round(u_o,2),"m/s**2"
```

In [10]:

```
import math
#Initilization of Variables
W1=100 #N #Weight of Block
W2=300 #N #weight of pulley
k=0.25 #m #Radius of gyration
r_A=0.2 #m #Radius of pulley A
r_B=0.3 #m #Radius of pulley B
g=9.81 #m/s**2 #Acceleration due to gravity
#Calculation
#Motion of block B
#(W1-T_B)=W1*g**-1*r_B*alpha ..................1
#Motion of block A
#(T_A-W1)=W1*g**-1*r_A*alpha ..................2
#M.I of pulley
I=W2*g**-1*k**2
#Rotation of pulley
#T_B*r_B-T_A*r_A=I*alpha .....................3
#After multiplying equation 1 by r_B we get
#30-r_B*T_B=W1*g**-1*r_B*alpha ..................4
#After multiplying equation 2 by r_A we get
#0.2*T_A-20=W1*g**-1*r_A*alpha ..................5
#Adding equations 3,4,5 and further simplifying we get
alpha=10*g*31.75**-1 #Rad/s**2
#Linear acceleration of pulley
alpha_B=0.3*alpha #m/s**2
alpha_A=0.2*alpha #m/s**2
#Tension in strings
T_A=W1+W1*g**-1*alpha_A #N
T_B=W1-W1*g**-1*alpha_B #N
#Result
print"Angular Acceleration of pulley",round(alpha,2),"rad/s**2"
print"Linear acceleration of blocks A and B:alpha_A",round(alpha_A,2),"rad/s**2"
print" :alpha_B",round(alpha_B,2),"rad/s**2"
print"Tension in the strings",round(T_A,2),"N"
print" ",round(T_B,2),"N"
```

In [48]:

```
import math
#Initilization of Variables
#Weights
W1=200 #N
W2=800 #N
F=400 #N #Force applied
mu=0.3 #Coefficient of friction
g=9.80 #m/s**2 #Acceleration due to gravity
#Calculation
#Total Weights
W=W1+W2 #N
#Total Mass
M=W*g**-1 #Kg
#Force of friction
F2=mu*W #N
#acceleration
a=-((-F+F2)*g)*W**-1 #m/s**2
#PArt-2
#Force of Friction
F3=mu*W1 #N
#Reverse Effective Force on it
F4=W1*g**-1*a #N
#Tension in thread
T=F3+F4 #N
#Result
print"acceleration of the weights is",round(a,2),"m/s**2"
print"Tension in the string is",round(T,2),"N"
```