In [1]:

```
#example 10.1
#calculation of the number of revolutions made
#given data
import math
wzero=100.*2.*math.pi/60.#initial angular velocity(in rad/s) of the motor
w=0#final angular velocity(in rad/s) of the motor
t=15.#time interval(in s)
#calculation
alpha=(w-wzero)/t#equation of angular motion
theta=(wzero*t)+(alpha*t*t/2.)#equation of angular motion
print '%s %.2f' %("the number of revolutions the motor makes before coming to rest is",theta/(2*math.pi))
```

In [2]:

```
import math
#example 10.2
#calculation of the time taken by the fan to attain half of the maximum speed
#given data
wzero=0#initial angular velocity(in rad/s) of the fan
w=400.*(2.*math.pi/60.)#final angular velocity(in rad/s) of the fan
t=5#tiem(in s) taken
#calculation
alpha=(w-wzero)/t#equation of angular motion
wdash=w/2.#half of maximum speed
t1=(wdash-wzero)/alpha#equation of angular motion
print '%s %.2f %s' %("the time taken by the fan to attain half of the maximum speed is",t1,"s")
```

In [3]:

```
import math
#example 10.3
#calculation of the angular velocity and angular acceleration of the pulley
#given data
v=20.#linear speed(in cm/s) of the bucket
r=10.#radius(in cm) of the pulley
a=4.*10.**2.#linear acceleration(in cm/s**2) of the pulley
#calculation
w=v/r#formula of angular velocity
alpha=a/r#formula of angular acceleration
print '%s %.2f %s %s %.2f %s' %("the angular velocity of the pulley is",w,"rad/s","and angular acceleration of the pulley is",alpha,"rad/s**2")
```

In [4]:

```
import math
#example 10.5
#calculation of the moment of inertia of the wheel
#given data
r=10.*10.**-2.#radius(in m) of the wheel
F=5.#force(in N) of pulling
aplha=2.#angular acceleration(in rad/s**2) of the wheel
#calculation
tau=F*r#net torque
I=tau/aplha#moment of inertia
print '%s %.2f %s' %("the moment of inertia of the wheel is",I,"kg-m**2")
```

In [5]:

```
import math
#example 10.12
#calculation of the kinetic energy of the sphere
#given data
M=200.*10.**-3.#mass(in kg) of the sphere
vcm=2.*10.**-2.#speed(in m/s) of the sphere
#calculation
#kinetic energy is K = (Icm*w*w/2) + (M*vcm*vcm/2)
#taking Icm = (2*M*r*r*w*w/5) and w=vcm/r
K=(M*vcm*vcm/5.)+(M*vcm*vcm/2.)#kinetic energy
print '%s %.5f %s' %("the kinetic energy of the sphere is",K,"J")
```

In [6]:

```
import math
#example 10.2w
#calculation of the angle rotated during the next second
#given data
theta=2.5#angular displacement(in rad) of the wheel
t=1.#time(in s) required
#calculation
alpha=(theta*2.)/(t*t)#equation of angular motion
theta1=(alpha*(t+1.)*(t+1.)/2.)#angle rotated during first two seconds
thetar=theta1-theta#angle rotated during next second
print '%s %.2f %s' %("the angle rotated during the next second is",thetar,"rad\n")
```

In [7]:

```
import math
#example 10.3w
#calculation of the torque required to stop the wheel in one minute
#given data
wzero=50.*(2.*math.pi/60.)#initial angular velocity(in rad/s) of the wheel
w=0#final angular velocity(in rad/s) of the wheel
t=60.#time(in s) taken to stop the wheel
I=2.#moment of inertia(in kg-m**2) of the wheel
#calculation
alpha=(w-wzero)/t#equation of angular motion
tau=I*abs(alpha)#torque
print '%s %.2f %s' %("the torque required to stop the wheel in one minute is",tau,"N-m")
```

In [8]:

```
import math
#example 10.4w
#calculation of the angular velocity of the wheel
#given data
F=20.#force(in N) of pull applied
I=.2#moment of inertia(in kg-m**2)
r=20.*10.**-2.#radius(in m) of the wheel
t=5.#time(in s) interval
wzero=0#initial angular velocity(in rad/s) of the wheel
#calculation
tau=F*r#torque applied to the wheel
alpha=tau/I#angular acceleration
w=wzero+(alpha*t)#equation of angular motion
print '%s %.2f %s' %("the angular velocity of the wheel after 5 s is",w,"rad/s")
```

In [9]:

```
import math
#example 10.7w
#calculation of the position of second kid on a balanced seesaw
#given data
ma=10.#mass(in kg) of kid A
mb=15.#mass(in kg) of kid B
l=5.#length(in m) of the seesaw
la=(l/2.)#distance of A kid from fulcrum as he is sitting at an end
#calculation
#taking torque about fulcrum...........(mb*g*x) = (ma*g*)
x=(ma*la)/mb
print '%s %.2f %s' %("the second kid should sit at a distance of",x,"m from the centre")
```

In [12]:

```
import math
#example 10.8w
#calculation of the normal force and the frictional force that the floor exerts on the ladder
#given data
m=10.#mass(in kg) of the ladder
theta=53.#angle(in degree) made by the ladder against the vertical wall
g=9.8#gravitational acceleration(in m/s**2) of the earth
#calculation
#taking horizontal and vertical components
#N1 = f........................(1)
#N2 = W........................(2)
#taking torque about B
W=m*g
N2=W#from equation (2)
f=(W*math.sin(theta)*57.3/2.)/(math.cos(theta)*57.3)#from equation (1)
print '%s %.2f %s' %("the normal force that the floor exerts on the ladder is",N2,"N\n")
print '%s %.2f %s' %("the frictional force that the floor exerts on the ladder is",f,"N\n")
```

In [11]:

```
import math
#example 10.9w
#calculation of the contact force exerted by the floor on each leg of ladder
#given data
theta=60.#angle(in degree) between the two legs
m=80.#mass(in kg) of the person
g=9.8#gravitational acceleration(in m/s**2) of the earth
#calculation
N=m*g/2.
T=(N*2.*math.tan(90-theta)*57.3)/1.
print '%s %.2f %s' %("the contact force exerted by the floor on each leg of ladder",N,"N\n")
print '%s %.2f %s' %("the tension in the crossbar is",T,"N\n")
```

In [13]:

```
import math
#example 10.13w
#calculation of the kinetic energy and angular momentum of the disc
#given data
M=200.*10.**-3.#mass(in kg) of the disc
r=4.*10.**-2.#radius(in m) of the disc
w=10.#angular velocity(in rad/s)
#calculation
I=(M*r*r)/4.#moment of inertia
K=(I*w*w/2.)#kinetic energy
L=I*w#angular momentum
print '%s %.2f %s' %("the kinetic energy of the disc is",K,"J")
print '%s %.2f %s' %("\nthe angular momentum of the disc is",L,"J-s\n")
```

In [14]:

```
import math
#example 10.14w
#calculation of the work done by the torque in first two seconds
#given data
wzero=20.#initial angular velocity(in rad/s) of the motor
w=0#final angular velocity(in rad/s) of the motor
t=4.#time(in s) taken to attain rest position
I=.20#moment of inertia(in kg-m**2) of the disc about axis of rotation
t1=2.#time(in s)
#calculation
alpha=(wzero-w)/t#equation of angular motion in case of deceleration
tau=I*alpha#torque
theta=(wzero*t1)-(alpha*t1*t1/2)#equation of angular motion
W=tau*theta#work done by the torque
print '%s %.2f %s' %("the work done by the torque in first two seconds is",W,"J")
```

In [15]:

```
import math
#example 10.19w
#calculation of the moment of inertia of the system about the axis perpendicular to the rod passing through its middle point
#given data
m=1.2#mass(in kg) of the sphere
R=10.*10.**-2.#radius(in cm) of the sphere
sep=50.*10.**-2.#separation(in m) between the two spheres
#calculation
d=sep/2.#distance of each sphere from centre
Icm=(2.*m*R*R)/5.#moment of inertia about diameter
I=Icm+(m*d*d)#by parallel axis theorem,moment of inertia about given axis
#since second sphere has same moment of inertia
Isys=2.*I#moment of inertia of the system
print '%s %.2f %s' %("the moment of inertia of the system about the axis perpendicular to the rod passing through its middle point is",Isys,"kg-m**2")
```

In [16]:

```
import math
#example 10.22w
#calculation of the number of revolutions made by the wheel per second
#given data
p=220.*10.**-2.#perimeter(in cm) of the wheel
v=9.*10.**3./(60.*60.)#linear speed(in m/s) of wheel on the road
#calculation
r=p/(2.*math.pi)#radius of the wheel
w=v/r#angular speed
n=w/(2.*math.pi)#number of revolutions
print '%s %.2f %s' %("the number of revolutions made by the wheel per second is",n,"rev/s\n")
```