# The rate of rotation of a solid disk with a radius of 8 m and mass of 5 kg constantly changes from 5 Hz to 17 Hz. If the change in rotational frequency occurs over 3 s, what torque was applied to the disk?

Nov 11, 2017

$\text{4021.2 Nm}$ of torque was applied to disc.

#### Explanation:

Torque is rate of change of angular momentum.

T = (I(omega_f - ω_i))/t

$= \frac{I 2 \pi \left({f}_{f} - {f}_{i}\right)}{t}$

$= \frac{\frac{m {r}^{2}}{2} 2 \pi \left({f}_{f} - {f}_{i}\right)}{t}$ ………[∵ Moment of inertia of disc about is central axis is $\frac{m {r}^{2}}{2}$]

= (("5 kg × (8 m)"^2)/2 × 2 π (17 - 5) "Hz")/"3 s" = "4021.2 Nm"