# An object with a mass of  2 kg is traveling in a circular path of a radius of 2 m. If the object's angular velocity changes from  3 Hz to  9 Hz in  1 s, what torque was applied to the object?

Apr 15, 2016

$96 \pi N m$

#### Explanation:

Comparing linear motion and Rotational motion for understanding

For Linear motion $- -$For rotational motion,

mass $\to$ moment of Inertial

Force $\to$ Torque

velocity $\to$ Angular velocity

acceleration $\to$ ANgular acceleration

So,

$F = m a$ $\to$ $\to$ $\tau = I \alpha$

Here,

$\alpha = \frac{{\omega}_{2} - {\omega}_{1}}{\Delta t} = \frac{2 \pi \times {n}_{2} - 2 \pi \times {n}_{1}}{\Delta t} = \left(2 \pi\right) \times \frac{\left(9 - 3\right)}{1} {s}^{- 2} = 12 \pi {s}^{- 2}$

and
$I = m {r}^{2} = 2 k g \cdot {2}^{2} {m}^{2} = 8 k g {m}^{2}$

So $\tau = 8 k g {m}^{2} \cdot 12 \pi {s}^{- 2} = 96 \pi N m$