Question

A turntable is switched from 11.3 rad/s to 1.9 rad/s, and the platter goes through an angle of 17.95 radian in reaching the new angular speed. What is the angular acceleration of the platter?

Answer 1

Hi there!

We can use the angular equivalent of the following kinematic equation:

$\omega_f^2 = \omega_i^2 + 2\alpha \theta$

ωf = final angular velocity (1.9 rad/s)

ωi = initial angular velocity (11.3 rad/s)

α = angular acceleration (? rad/s²)

θ = angular displacement (17.95 rad)

We can rearrange the equation to solve for angular acceleration.

$\omega_f^2 - \omega_i^2 = 2\alpha \theta\\\\\alpha = \frac{\omega_f^2 - \omega_i^2}{2\theta}$

Plug in the given values and solve.

$\alpha = \frac{1.9^2 - 11.3^2}{2(17.95)} = \boxed{3.456 \frac{rad}{s}}$