An object with a mass of # 2 kg# is traveling in a circular path of a radius of #2 m#. If the object's angular velocity changes from # 1 Hz# to # 4 Hz# in # 1 s#, what torque was applied to the object?

1 Answer
Dec 25, 2016

Answer:

The torque is #=75.4Nm#

Explanation:

The torque is the rate of change of angular momentum

#tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt#

The is #I=1/2mr^2#

#=1/2*2*2^2= 4 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(4-1)/1*2pi#

#=6pi rads^(-2)#

So the torque is #tau=4*6pi Nm=24piNm=75.4Nm#