In [1]:

```
#given
w=4 #Angular velocity in rad/s
m=(1,2,3,4) #Masses in kg from the figure 4.17 on page no.54
r=(2.5,1.5) #Centre position in m
#Calculations
I=(m[0]+m[1]+m[2]+m[3])*(r[0]**2+r[1]**2)
KE=(1/2.0)*I*w**2
#Output
print"The moment of inertia is ",I,"kg.m**2"
print"Kinetic energy of the system is ",KE,"J"
```

In [3]:

```
#given
q=30 #Angle of inclination in degrees
h=1 #Height in m
#Calculations
import math
v=math.sqrt((10/7.0)*9.8*h)
a=(5/7.0)*9.8*math.sin(q*3.14/180.0)
#Output
print"Velocity and acceleration of the centre of mass of the sphere is ",round(v,2),"m/s and ",round(a,1),"m/s**2"
```

In [4]:

```
#given
m=1.2 #Mass of the rod in kg
l=0.8 #Length of the rod in m
#Calculations
import math
T=2*3.14*math.sqrt((2*l)/(3.0*9.8))
#Output
print"Period of oscillation is ",round(T,2),"s"
```

In [5]:

```
#given
r=0.2 #Radius of uniform disc in m
d=0.15 #Distance from the centre in m
#Calculations
import math
T=2*3.14*math.sqrt((17*r)/(12.0*9.8))
#Output
print"The period of oscillation is ",round(T,3),"s"
```

In [6]:

```
#given
m=3 #Mass of the rotor in kg
I=0.03 #Moment of inertia in kg.m^2
d=0.25 #Distance of pivot from the centre in m
p=30 #Precession in rpm
#Calculations
T=m*9.8*d
w=(p*2*3.14)/60.0
w1=(T/(I*w))
#Output
print"Angular speed of rotation of the rotor is ",round(w1,0),"rpm"
```