Chapter 8, Problem 101A

To determine

To Write: A physics problem with real life objects for which the given equation would be part of solution.

Explanation of Solution

Introduction:

As per second equation of rotational motion:

  $\Delta \theta =\omega t+\frac{1}{2}\alpha t^2$

Here, $\theta$ is the angular displacement, $\omega$ is the initial angular velocity, $\alpha$ is the angular acceleration and t is the time.

A wheel has initial rotational velocity $20\text{rad/s}$ which comes to stop in 4 s with angular deceleration of $3.5{\text{rad/s}}^{\text{2}}$ . Find the angular displacement of the wheel in this duration.

Solution of this problem would involve the equation:

  $\Delta \theta =\left(20\frac{\text{rad}}{\text{s}}\right)\left(4\text{s}\right)-\frac{1}{2}\left(\text{3}\text{.5}\frac{\text{rad}}{{\text{s}}^{\text{2}}}\right){\left(\text{4}\text{s}\right)}^2$