Chapter 21:Motion of Rotation

Example 21.1, Page no.447

In [1]:
#variable declaration
omega_0=0     #initial angular velocity
alpha=0.5     #angular acceleration in rad/sec**2
t=10          #time in sec

#calculation
omega=omega_0+alpha*t
theta=omega_0*t+(alpha*t**2/2)

#Result
print"Angular velocity of the flywheel, omega=",int(omega),"rad/sec"
print"Angular displacement of the flywheel, theta=",int(theta),"rad"

Angular velocity of the flywheel, omega= 5 rad/sec
Angular displacement of the flywheel, theta= 25 rad

Example 21.4, Page no.448

In [2]:
import math
#variable declaration
omega_0=0     #initial angular velocity
alpha=0.5     #acceleration in rad/sec**2
t_1=120       #timetaken in sec
omega1_0=60   #initial angular velocity when pulley is coming to rest in rad/sec
alpha_2=-0.3  #Retardation in rad/sec**2


#calculation
#To calculate angular speed of pully in r.p.m. at the end of 2 min.
omega=round((omega_0+alpha*t_1)/(2*math.pi),2)
#To calculate time in which the pulley will come to rest
t_2=-omega1_0/alpha_2

#Result
print"Angular speed of pully in r.p.m. at the end of 2 min., omega=",int(omega*60),"r.p.m."
print"Time in which the pulley will come to rest, t_2=",int(t_2),"sec"

Angular speed of pully in r.p.m. at the end of 2 min., omega= 573 r.p.m.
Time in which the pulley will come to rest, t_2= 200 sec

Example 21.9, Page no.453

In [3]:
#variable declaration
r=0.6      #radius of wheel in m
omega_0=0  #initial angular velocity
alpha=0.8  #angular acceleration in rad/s**2
t=5        #time in s

#calculation
omega=omega_0+alpha*t
v=r*omega

#result
print"Linear velocity of the point on the periphery of the wheel, v=",round(v,1),"m/s"

Linear velocity of the point on the periphery of the wheel, v= 2.4 m/s

Example 21.10, Page no.453

In [4]:
import math
#variable declaration
r=1    #Radius if pulley in m
N=240  #angular frequency in r.p.m

#calculation
omega=2*math.pi*N/60
v=r*omega

#Result
print"Linear velocity of the particle on the periphery of the wheel, v=",round(v,1),"m/s"

Linear velocity of the particle on the periphery of the wheel, v= 25.1 m/s
In [ ]: