Question

A 0.32 kg turntable of radius 0.18 m spins about a vertical axis through its center. A constant rotational acceleration causes the turntable to accelerate from 0 to 24 revolutions per second in 8.0 s. [Hint: model the turntable has a uniform density disk.] What is the rotational acceleration of the turntable

Answer 1

Answer:$18.85 rad/s^2$

Explanation:

Given

mass of turntable $m=0.32 kg$

radius $r=0.18 m$

$N=24 rev/s$

$\omega =2\pi N=2\pi 24$

$\omega =48\pi rad/s$

time interval $t=8 s$

using $\omega =\omeag _0+\alpha t$

where $\omega =final\ angular\ velocity$

$\omega _0=initial\ angular\ velocity$

$\alpha =angular\ acceleration$

$t=time$

$48\pi =0+\alpha \times 8$

$\alpha =6\pi rad/s^2$

$\alpha =18.85 rad/s^2$