Question

An object with a mass of `2 kg` is traveling in a circular path of a radius of `4 m`. If the object's angular velocity changes from `1 Hz` to `12 Hz` in `2 s`, what torque was applied to the object?

Answer 1

`T=352pi " "N*m`

Explanation:

`m=2" "kg" mass of object"`

`r=4" "m " radius of the circular path"`

`f_1=1" "Hz" initial frequency of object"`

`f_2=12" "Hz" final frequency of object"`

`Delta t=2" "s`

`F=m*a " Newton equation for linear motion"`

`T=I*alpha" Newton equation for rotary motion"`

`T " represents Torque of object"`

`I " represents the moment of inertia of the object"`

`alpha " represents angular acceleration of the object"`

`alpha=(omega_2-omega_1)/(Delta t)`

`"the angular velocity of an object is expressed as "omega=2*pi*f`

`alpha=(2*pi(f_2-f_1))/2=pi(f_2-f_1)=pi(12-1)=11pi`

`I=m*r^2=2*4^2=32`

`T=32*11pi`

`T=352pi " "N*m`