Question

A flywheel with a radius of 0.200m starts from rest and accelerates with a constant angular acceleration of 0.900rad/s2.

Answer 1

Answer:

The magnitude of the radial acceleration is 0.754 rad/s²

Explanation:

Given;

radius of the flywheel, r = 0.2 m

initial angular velocity of the flywheel, $\omega_i = 0$

angular acceleration of the flywheel, a = 0.900 rad/s².

angular distance, θ = 120⁰

the angular distance in radian = $\frac{120}{180} \pi = \frac{2 \pi}{3} \ rad$

Apply the following kinematic equation to determine the final angular velocity;

$\omega _f^2 = \omega _i ^2 + 2\alpha \theta\\\\\omega _f^2 = 0 + 2(0.9)(\frac{2\pi}{3} )\\\\\omega _f^2 = 3.7699\\\\\omega _f = \sqrt{ 3.7699} \\\\ \omega _f = 1.942 \ rad/s$

The magnitude of the radial acceleration is calculated as;

$\alpha _r = \omega ^2r\\\\\alpha _r = (1.942)^2 (0.2)\\\\\alpha _r =0.754 \ rad/s^2$

Therefore, the magnitude of the radial acceleration is 0.754 rad/s²