Question

A wheel having a diameter of 3m starts from rest and accelerate uniformly to an angular velocity of 210 rpm in 5 second angular acceleration of wheel is t

Answer 1

Let x be denoted as angular velocity

Then,

Angular acceleration = (dx)/ dt

Angular acceleration= ((210-0)/(5-0)) × (1/60)

=7/10

=0.7

This is the required angular acceleration

Answer 2

A wheel having a diameter of 3m starts from rest and accelerate uniformly to an angular velocity of 210 rpm in 5 second.
we have to find angular acceleration.

initial angular velocity,$\omega_0$=0
final angular velocity, $\omega$=210rpm
= 210 × 2π/60 rad/sec
= 210 × 2 × 22/(7 × 60)
= 22 rad/sec

use formula, $\omega=\omega_0+\alpha t$
22 = 0 + $\alpha$ × 5

$alpha=\frac{22}{5}=4.4rad/s^2$