Question

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During a 5.0-s interval, the angular velocity decreases to 10 rad/s. Assume that the angular acceleration is constant during the 5.0-s interval. How many radians does the wheel turn through during the 5.0-s interval

Answer 1

Answer:

The angular displacement of the wheel is 45 radians

Explanation:

Given;

initial angular velocity, ω₀ = 20 rad/s

final angular velocity, ωf = 10 rad/s

time interval, t = 5

Angular acceleration is calculated as;

$\alpha = \frac{\omega _f - \omega_0}{t} \\\\\alpha = \frac{10 -20}{5} \\\\\alpha = -2 \ rad/s^2$

|α| = 2 rad/s²

Angular displacement is calculated as;

$\theta = \omega_0 \ + \ \frac{1}{2} \alpha t^2\\\\\theta = 20 \ + \ \frac{1}{2} *(2)*5^2\\\\\theta = 20 \ + 25\\\\ \theta = 45 \ radians$

Therefore, the angular displacement of the wheel is 45 radians