A pulley of radius 15 cm rotates 5 times in 64 seconds. Find the angular speed of the pulley.
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 \(\bf \cfrac{5rev}{64s}\implies \cfrac{10\pi }{64}\implies \cfrac{5\pi }{32}\)
The angular speed of the pulley, which rotates 5 times in total 64 seconds is 5π/32 rad/sec.
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.
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