Chapter 4 Rotational motion of Rigid objects

Example 4.1 Page no 54

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"

The moment of inertia is  85.0 kg.m**2
Kinetic energy of the system is  680.0 J

Example 4.2 Page no 55

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"

Velocity and acceleration of the centre of mass of the sphere is  3.74 m/s and  3.5 m/s**2

Example 4.3 Page no 55

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"

Period of oscillation is  1.47 s

Example 4.4 Page no 55

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"

The period of oscillation is  1.068 s

Example 4.5 Page no 55

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"

Angular speed of rotation of the rotor is  78.0 rpm