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`

Step-by-step 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 * 8`

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

`\alpha =18.85 rad/s^2`