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 # 3 Hz# to # 7 Hz# in #3 s#, what torque was applied to the object?

1 Answer
Jul 17, 2017

Answer:

We will use cassical mechanics (rotation) equations to solve this problem.

Explanation:

With frequency of #3Hz# the velocity is #ω_1=2pif_1=6pi(rads)/s#

With frequency of #7Hz# the velocity is #ω_2=2pif_2=14pi(rads)/s#

The angular acceleration is then

#α=(Δω)/(Δt)=(14pi-6pi)/3=(8pi)/3(rads)/s^2#

and the torque is :

#Τ=Iα=mr^2α=3*49*(8pi)/3=392piNm#