# An object with a mass of  6 kg is traveling in a circular path of a radius of  1m. If the object's angular velocity changes from  6 Hz to  7 Hz in 3 s, what torque was applied to the object?

$\setminus \tau = 12.562 N \setminus \cdot m$

#### Explanation:

First, convert the given angular velocities to $\frac{r a d}{s}$ where $1 H z = \left(2 \setminus \pi\right) \frac{r a d}{s}$
Therefore,
$6 H z = 37.699 \frac{r a d}{s}$
$7 H z = 43.98 \frac{r a d}{s}$

Torque is
$\setminus \tau = F l = m a l$

Finding for the tangential acceleration, use
$v = {v}_{0} + a t$
where $a = 2.09367 \frac{m}{s} ^ 2$

Therefore,
$\setminus \tau = \left(6 k g\right) \setminus \cdot \left(2.09367 \frac{m}{s} ^ 2\right) \setminus \cdot \left(1 m\right)$
$\setminus \tau = 12.562 N \setminus \cdot m$