# 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 # 4 Hz# to # 5 Hz# in # 3 s#, what torque was applied to the object?

##### 1 Answer

We will need to know the angular acceleration that existed during those 3 s. If this was a linear motion problem we could use the suvat formula

The equivalent formula in angular motion is

Using that last formula,

Solving for

Next we need the angular motion equivalent of F=m*a (Newton's 2nd Law). The equivalent is

I will assume the object can be considered a point mass. This requires that the dimensions of the object be much smaller than the 4 m radius. With that assumption, the rotational inertia,

So now we can calculate the torque,

You might ask how the combination of units

Torque is the product of force and the length of the lever arm. So, we have our answer.

I hope this helps,

Steve