Question

A wheel having a diameter of 3m start from rest and accelerates uniformly to an angular velocity of 210r.p.m in 5Second. Angular acceleration of the wheel is

Answer 1

application of Newton's second law of motion in rotational motion

Answer 2

The angular acceleration of the wheel is $4.39\ rad/s^2$.

Explanation:

Given that,

Initial speed of the wheel, $\omega_i=0$

Final speed of the wheel, $\omega_f=210\ rpm=21.99\ rad/s$

Time, t = 5 s

To find,

The angular acceleration of the wheel.

Solution,

The rate of change of angular velocity of any object is called its angular acceleration. It is given by :

$\alpha =\dfrac{\omega_f-\omega_i}{t}$

$\alpha =\dfrac{21.99-0}{5}$

$\alpha =4.39\ rad/s^2$

So, the angular acceleration of the wheel is $4.39\ rad/s^2$.

learn more,

Rotational kinematics

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