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

Mar 25, 2016

$294 N \cdot m$

#### Explanation:

The torque is the product between the inertial momentum and the angular acceleration $\tau = I \cdot \alpha$.

As this case is single particle in a circular path $I = m \cdot {r}^{2}$ and

$\omega = \frac{\Delta \omega}{\Delta t}$, so

$\tau = m \cdot r \cdot \frac{\Delta \omega}{\Delta t} = 3 k g \cdot 49 {m}^{2} \cdot \frac{9 H z - 3 H z}{3 s g} = 294 N \cdot m$