Question

A pulley of radius 15 cm rotates 5 times in 64 seconds. Find the angular speed of the pulley.

Answer 1

well... hmmm one time around will be a revolution or $2\pi$

now, this pulley has done 5 revolutions in 64 seconds, that will be its "angular speed" or $\bf \cfrac{5rev}{64s}\implies \cfrac{10\pi }{64}\implies \cfrac{5\pi }{32}$

Answer 2

The angular speed of the pulley, which rotates 5 times in total 64 seconds is 5π/32 rad/sec.

What is angular speed of a body?

The angular speed of a body is the rate by which the body changed its angle with respect to the time. It can be given as,

$\omega= \dfrac{\Delta \theta}{\Delta t}$

Here, ($\Delta$$\theta$) is the change in angle, and (t) is the time.

The pulley of radius 15 cm long. This pulley rotates 5 times in 64 seconds. As, one rotation is of 2π. Therefore, the angular acceleration is,

$\omega=\dfrac{2\pi \times5}{64}\\\omega=\dfrac{5\pi}{32}$

Hence, the angular speed of the pulley, which rotates 5 times in total 64 seconds is 5π/32 rad/sec.

Learn more about the angular speed here;

https://brainly.com/question/540174