Question

(5 points) A spinning ball has an angular velocity of wo. After it spins through an angle It has angular velocity ay. (a) (1 point) Solve for angular acceleration. (b) (1 point) Average angular velocity (c) (1 point) How much time elapsed? (d) points) Given wo- 7.2 +23 rad (CCW), find a and t. (2 rad/s CCW (or +2), w-+1.4 rad/s CCW, and θ-

Answer 1

We use angular variable to describe the motion of a body in case if the there is circular motion. In question when ball spins in through angle it starts moving in circular motion with angular variables.

We use angular variable to describe the motion of a body in case if the there is circular motion. In question when ball spins in through angle it starts moving in circular motion with angular variables. Given, initial angular velocity = w_0 final angular velocity = w_f angular position = theta (a) Angular acceleration (alpha): use equal t^n: w^2_f = w^2_0 + 2 alpha theta 2 alpha theta = w^2_f - w^2_0 alpha = w^2_f - w^2_0/2 theta (b) Average angular velocity (w_avg) w_avg = w_0 + w_f/2 (c) Time elapsed (t) use theta = w_0 t + 1/2 alpha t^2 (d) Given w_0 = 7.2 rad/s, w_f = 1.4 rad/s theta = 23 rad alpha = w^2_f - w^2_0/2 theta = 1.4^2 - 7.2^2/2 times 23 = -1.084 rad/s^2 negative sign shows angular velocity is decreasing in the direction of motion: so, alpha = -1.84 rad/s^2 for t: theta = w_0 t + 1/2 alpha t^2 23 rad = 7.2 t + 1/2 (-1.084) t^2 = 7.2 t - 0.542 t^2 rightdoublearrow 0.542 t^2 - 7.2 t + 23 = 0 on solving, we get t = 7.94 sec or t = 5.34 sec