Question

Suppose David puts a 0.60 kg rock into a sling of length 1.6 m and begins whirling the rock in a nearly horizontal circle, accelerating it from rest to a rate of 120 rpm after 5.7 s .
Part A
What is the torque required to achieve this feat?
Express your answer using three significant figures and include the appropriate units.
Part B
Where does the torque come from?

Answer 1

A. Moment of inertia of whirling rock:

$$I=mr^2=(0.6)(1.6)^2=1.536 kgm^2$$

$$\Delta \omega =\frac{2\pi (120)}{60}=4\pi rad/s$$

$$\alpha=\frac{\Delta \omega}{\Delta t}=\frac{4\pi}{5.7}=2.2 rad/s^2$$

The torque required to achieve this feat:

$$\tau=I\alpha=1.536(2.2)=3.4 Nm$$

B. The torque come from David's force.