# An object with a mass of  3 kg is traveling in a circular path of a radius of 15 m. If the object's angular velocity changes from  25 Hz to  28 Hz in 9 s, what torque was applied to the object?

Angular acceleration $\alpha = \frac{{\omega}_{f} - {\omega}_{i}}{t} = 2 \pi \left(\frac{{n}_{f} - {n}_{i}}{t}\right) = 2 \pi \frac{28 - 25}{9} = \frac{2 \pi}{3} r a {\mathrm{ds}}^{-} 2$
$I = m {r}^{2} = 3 \times {15}^{2} = 675 k g {m}^{2}$
$\tau = I \times \alpha = 675 \times \frac{2 \pi}{3} = 450 \pi J$