Question

The initial angular velocity and angular acceleration of four rotating objects at the same instant in time are listed in the table that follows. For each of the object determine the final angular speed after an elapsed time of 2.1 s​

Answer 1

Explanation:

The elapsed time, t = 2.1 s

(a) Initial angular velocity, $\omega_0=12.4\ rad/s$ and angular acceleration, $\alpha =4\ rad/s^2$

Final angular velocity,

$\omega_f=\omega_i+\alpha t\\\\\omega_f=12.4+4(2.1)\\\\\omega_f=20.8\ rad/s$

(b)  Initial angular velocity, $\omega_0=12.4\ rad/s$ and angular acceleration, $\alpha =-4\ rad/s^2$

Final angular velocity,

$\omega_f=\omega_i+\alpha t\\\\\omega_f=12.4+(-4)(2.1)\\\\\omega_f=4\ rad/s$

(c) Initial angular velocity, $\omega_0=-12.4\ rad/s$ and angular acceleration, $\alpha =4\ rad/s^2$

Final angular velocity,

$\omega_f=\omega_i+\alpha t\\\\\omega_f=-12.4+(4)(2.1)\\\\\omega_f=-4\ rad/s$

(d) Initial angular velocity, $\omega_0=-12.4\ rad/s$ and angular acceleration, $\alpha =-4\ rad/s^2$

Final angular velocity,

$\omega_f=\omega_i+\alpha t\\\\\omega_f=-12.4+(-4)(2.1)\\\\\omega_f=-20.8\ rad/s$