Question

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest. What is the angular velocity at the end of that time?

Answer 1

Answer:

$\omega_f = 3.584\ rad/s$

Explanation:

given,

turntable rotate to, θ = 5 rad

time, t = 2.8 s

initial angular speed  = 0 rad/s

final angular speed = ?

now, using equation of rotational motion

$\theta = \omega_i t + \dfrac{1}{2}\alpha t^2$

$5 = 0+ \dfrac{1}{2}\alpha\times 2.8^2$

$\alpha= \dfrac{10}{2.8^2}$

       α = 1.28 rad/s²

now, calculation of angular velocity

$\omega_f = \omega_i + \alpha t$

$\omega_f =0 +1.28\times 2.8$

$\omega_f = 3.584\ rad/s$

hence, the angular velocity at the end is equal to 3.584 rad/s