Question

The time it takes for a disk to rotate 45 revolutions is 5.82 s. The angular velocity at the end of the 5.82 s time interval is 68 rad⋅s−1.a) Calculate the constant angular acceleration (in rad⋅s−2) of the disk.

Answer 1

Given data

*The given time is t = 5.82 s

*The given angular velocity is

`\omega=68\text{ rad/s}`

*The number of the revolution is n = 45 revolutions

*The angular distance traveled is

`\theta=2\pi n=2\pi(45)=90\pi\text{ rad}`

(a)

The formula for the constant angular acceleration is given by the rotational equation of motion as

`\theta=\omega t-(1)/(2)\alpha t^2`

Substitute the known values in the above expression as

`\begin{gathered} 90\pi=(68)(5.82)-(1)/(2)\alpha(5.82)^2 \\ \alpha=6.68rad.s^(-2) \end{gathered}`

Hence, the constant angular acceleration of the disk is 6.68 rad/s^2.