import math
#Initilization of Variables
w_o=5 #Rad/s #Initial Angular Velocity
w=13 #rad/s #IFinal angular Velocity
t=4 #s #time
#Calculation
#Angular Acceleration of the body
alpha=(w-w_o)*t**-1 #rad/s**2
#Result
print"Angular Acceleration of the body is",round(alpha,2),"Rad/s**2"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
N_o=20 #Initial r.p.m of wheel
n=50 #No. of revolution
n2=100
t=70 #s #time
#Calculation
#Angular Dispalcement
theta=2*pi*n
#Initial Angular Velocity
w_o=2*pi*N_o*60**-1
#Angular Velocity at the end of 70 s
alpha=(theta-w_o*t)*((t**2)*2**-1)**-1 #rad/s**2
w=w_o+alpha*t #rad/s
#Time Required for the speed to reach 100 r.p.m
#Final Angular Velocity
w2=2*pi*n2*60**-1 #rad/s
#Time required for speed to reach 100 revolutions
t=(w2-w_o)*alpha**-1 #s
#Result
print"Angular Velocity at the end of 70 s is",round(w,2),"rad/s**2"
print"Time required for speed to reach 100 revolutions is",round(t,2),"s"
import math
#Initilization of Variables
alpha=1 #rad/s**2 #Angular Acceleration
w_o=5.25 #rad/s**2 #Initial Angular velocity
w=10.50 #rad/s**2 #Final angular velocity
#Calculation
#Total angle turned
theta=(w**2-w_o**2)*2**-1 #rad
#Result
print"Total angle turned is",round(theta,2),"rad"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
#Part-1
w_o=0 #Initial angular velocity
alpha=1 #rad/s**2 #Angular accleration
t=90 #s #time
#Part-2
w_o2=90 #rad/s #Initial Angular velocity
w2=0 #final angular velocity
alpha2=-0.5 #rad/s**2 #Angular retardation
#Calculation
#Part-1
#Angular Velocity
w=w_o+alpha*t #rad/s
#Speed in r.p.m
N=60*w*(2*pi)**-1 #r.p.m
#Part-2
#Time taken by flywheel in seconds to come to rest
t1=-w_o2*alpha2**-1 #s
#Result
print"Speed in r.p.m is",round(N,2)
print"Time taken by flywheel in seconds to come to rest is",round(t1,2),"s"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
N=200 #r.p.m #initial speed
f1=20.94 #rad/s #Frequency
N2=160 #r.p.m
t=10 #s #time
f2=16.75 #rad/s
f3=0 #Final angular velocity
#Calculation
#Uniform retardation
alpha=(f2-f1)*t**-1 #rad/s**2
#total angular displacement
theta=(f3**2-f1**2)*(2*alpha)**-1 #rad
n=theta*(2*pi)**-1 #revolutions
#Time taken by wheel before it comes to rest
t=-f1*alpha**-1
#Result
print"Number of revolutions is",round(n,2),"revolution"
print"Time taken by wheel before it comes to rest is",round(t,2),"s"
import math
#Initilization of Variables
#Angle of rotation
#theta=2*t**3-5*t**2+8*t+6
t=0 #s
t2=4 #s
#Calculation
#After deriving above equation we get
f1=6*t**2-10*t+8 #rad/s
#Again differentiating above equation we get
alpha1=12*t-10 #rad/s**2
#for t2=4
f2=6*t2**2-10*t2+8 #rad/s
alpha2=12*t2-10 #rad/s**2
#Result
print"Angular Velocity at t=0 is",round(f1,2),"rad/s"
print"Angular acceleration at t=4 is",round(alpha1,2),"rad/s**2"
print"Angular Velocity at t=0 is",round(f2,2),"rad/s"
print"Angular acceleration at t=4 is",round(alpha2,2),"rad/s**2"
import math
#Initilization of Variables
#angular rotation
#theta=9*32**-1*t**3
t=1.6 #s
#Calculation
#after differentiating above equation twice we get
alpha=27*16**-1*t #rad/s**2
#Result
print"Angular accelerations is",round(alpha,2),"rad/s**2"
import math
#Initilization of Variables
f1=2 #rad/s #initiaal angular velocity
alpha1=0 #Initial angular acceleration
#Calculation
#Integrating law of rotation we get
#f2=t**3-3*t+C .......1
#put t=0 weg et
C=2
#now at t=5 #s
t=5 #s
f2=t**3-3*t+C
#Integrting equation 1 we get
#theta=t**4*4**-1-3*t**2*2**-1+2*t
#Sub values and further simplifying we get
theta=t**4*4**-1-3*t**2*2**-1+2*t
#Result
print"Angular velocity when t=5s is",round(f2,2),"rad/s"
print"Angular displacement when t=5s is",round(theta,2),"radians"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
#Angle of rotation of body
#theta=theta1+a*t+b*t**2
f=3*pi
f2=8*pi
t=0 #s
t2=2 #s
#Calculations
#differentiating above equation and further sub values and simplifuing we getweget
a=f
b=(f2-a)*4**-1
#Result
print"Constants a is",round(a,2)
print"Constants b is",round(b,2)
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
#Velocity
V_A=4 #m/s
theta=30 #Degrees
#Calculation
#Velocity
V_B=V_A*(tan(theta*pi*180**-1))**-1 #m/s
#Result
print"Velocity of point B is",round(V_B,2),"m/s"
import math
#Initilization of Variables
r=1 #m #radius
V_C=20 #m/s #Velocity
f=20 #rad/s #Angular velocity
#Calculation
#Length
L_DE=(r**2+r**2)**0.5 #m
L_DF=2 #m #Diameter
#Velocity
V_E=L_DE*f #m/s
V_F=f*L_DF #m/s
#Result
print"Velocity of point E:V_E",round(V_E,2),"m/s"
print"Velocity of point E:V_F",round(V_F,2),"m/s"
import math
#Initilization of Variables
D=50 #cm
r=0.25 #m #radius
V_A=L_AL=5 #m/s
V_B=L_BM=3 #m/s
#Calculation
#V_A=f*L_AO
#V_B=f*L_BO
#After further simplifying and resolving we get
f=2*0.5**-1 #rad/s
x=L_BO=3*f**-1
#Linear Velocity
V_C=f*(r+x) #m/s
#Result
print"Linear Velocity of roller is",round(V_C,2),"m/s"
print"Angular velocity is",round(f,2),"rad/s"
import math
from math import sin, cos, tan, radians, pi
#Initilization of Variables
r=1 #m
u=20 #m/s
#Calculation
#Velocity component of point E
#u_E=u+u*sin(u*t)
#at t=0
t=0
u_E=u+u*sin(u*t*pi*180**-1)
v_E=u*cos(u*t)
V_E=(u_E**2+v_E**2)**0.5 #m/s
u_F=u+u*cos(u*t*pi*180**-1) #m/s
#Result
print"Velocity of point E is",round(V_E,2),"m/s"
print"Velocity of point F is",round(u_F,2),"m/s"
import math
#Initilization of Variables
g=9.81 #Acceleration due to gravity
W1=W2=80*1000*g
D1=0.75*10**3 #mm
R1=0.75*500 #mm
a1=0.025 #m/s**2
D2=1.2*10**3 #mm
R2=1.2*500 #mm
a2=0.0625 #m/s**2
#Calculation
#Horizontal Forces
P1=W1*a1*R1**-1 #N
P2=W2*a2*R2**-1 #N
#Result
print"Horizontal Force required to maintain uniform speed is",round(P1,2),"N"
print"Horizontal Force for truck and trailer is",round(P2,2),"N"