Question

How long does it take for a rotating object to speed up from 15.0 sto 33.3 rad/s if it has an angular acceleration of 3.45rad/s2?
a) 9.57 s
b) 5.30 s
c) 63.1 s
d) 4.35 s

Answer 1

Answer:

The time taken by the rotating object to speed up from 15.0 s to 33.3 rad/s is 5.30 seconds.        

Explanation:

It is given that,

Initial angular speed of the object, $\omega_o=15\ rad/s$

Final angular speed of the object, $\omega_f=33.3\ rad/s$

Angular acceleration of the object, $\alpha =3.45\ rad/s^2$

Angular acceleration of an object is object is defined as the change in angular velocity per unit time. It is given by :

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

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

$t =\dfrac{33.3-15}{3.45}$

t = 5.30 seconds

So, the time taken by the rotating object to speed up from 15.0 s to 33.3 rad/s is 5.30 seconds. Hence, this is the required solution.