Question

A 30 cm diameter turn table starts
from rest and takes 2 s to reach its final
rotation rate of 33.5 rpm; the angular
acceleration is​

Answer 1

Given:

A 30 cm diameter turn table starts

from rest and takes 2 s to reach its final

rotation rate of 33.5 rpm.

To find:

Angular acceleration.

Calculation:

$\boxed{33.5 \: rpm = \dfrac{33.5 \times 2\pi}{60} = 1.1\pi \: rad {s}^{ - 1} }$

Now , applying equations of rotational kinematics:

$\therefore \: \omega2 = \omega1 + \alpha t$

$= > \: 1.1\pi = 0 + \alpha (2)$

$= > \: \alpha (2) = 1.1\pi$

$= > \: \alpha = \dfrac{1.1\pi}{2}$

$= > \: \alpha = 0.55\pi$

$= > \: \alpha = 0.55 \times 3.14$

$= > \: \alpha = 1.75 \: rad {s}^{ - 2}$

So, final answer is:

$\boxed{ \red{ \bold{\: \alpha = 1.75 \: rad {s}^{ - 2} }}}$