# What torque would have to be applied to a rod with a length of 3 m and a mass of 1 kg to change its horizontal spin by a frequency of 3 Hz over 2 s?

Feb 4, 2017

The torque $= 7.07 N m$

#### Explanation:

The torque is the rate of change of angular momentum

$\tau = \frac{\mathrm{dL}}{\mathrm{dt}} = \frac{d \left(I \omega\right)}{\mathrm{dt}} = I \frac{\mathrm{do} m e g a}{\mathrm{dt}}$

The moment of inertia of a rod is $I = \frac{1}{12} \cdot m {L}^{2}$

$= \frac{1}{12} \cdot 1 \cdot {3}^{2} = \frac{3}{4} k g {m}^{2}$

The rate of change of angular velocity is

$\frac{\mathrm{do} m e g a}{\mathrm{dt}} = \frac{3}{2} \cdot 2 \pi$

$= \left(3 \pi\right) r a {\mathrm{ds}}^{- 2}$

So the torque is $\tau = \frac{3}{4} \cdot \left(3 \pi\right) N m = \frac{9}{4} \pi N m = 7.07 N m$