Question

A torsional pendulum consists of a disk of mass 450 g and radius 3.5 cm, hanging from a wire. If the disk is rotated through an angle of 45o and released from rest and oscillates with a frequency of 2.5 Hz, what is maximum angular speed of the disk?

Answer 1

Answer:12.34 rad/s

Step-by-step explanation:

We know in torsional pendulum

`I\ddot{\theta }=-k\theta`

`\ddot{\theta }+\omega ^2\theta =0`

`\omega ^2=(k)/(I)`

general equation of it

`\theta \left ( t\right )=\theta _0cos\omega t`

and at t=0 \theta =45[/tex]

`(\pi )/(4)=\theta _0`

`\theta \left ( t\right )=(\pi )/(4)cos\omega t`

and
`\omega =2\pi f=5\pi`

For angular velocity

`\frac{\mathrm{d}\theta }{\mathrm{d}t}=-(5\pi ^2)/(4)sin5\pi t`

Maximum angular velocity=
`(5\pi ^2)/(4)=12.34 rad/s`