An object with a mass of # 3 kg# is traveling in a circular path of a radius of #7 m#. If the object's angular velocity changes from # 13Hz# to # 17 Hz# in #5 s#, what torque was applied to the object?

1 Answer
Jun 27, 2018

Answer:

The torque was #=738.9Nm#

Explanation:

The torque is the rate of change of angular momentum

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

For the object, the moment of inertia is

#I=mr^2#

The mass of the disc is #m=3 kg#

The radius of the disc is #r=7m#

The moment of inertia is

#I=3*7^2=147kg m^2#

The angular acceleration is

#alpha=2pi(f_2-f_1)/t=2pi(17-13)/5=1.6pirads^-2#

The torque is

#tau=I omega=147*1.6pi=738.9Nm#