Question

A disk with an initial angular velocity ω0 = 6.5 rad/s experiences a constant angular acceleration of α = 6.5 rad/s² for a time period t = 15 s. Please answer the following questions.

Write an expression for the magnitude of the angular velocity of the disk at time t in terms of the given parameters.

Answer 1

The expression for the magnitude of the angular velocity of the disk at time t is ω = ω0 + αt. By substituting the given values, the final angular velocity at t = 15 s is calculated to be 104.0 rad/s.

Step-by-step explanation:

The student is asking to find the final angular velocity of a disk given an initial angular velocity (ω0), a constant angular acceleration (α), and a time period (t). Using the kinematic equation for rotational motion, ω = ω0 + αt, where ω is the final angular velocity, we can plug in the given values to find the answer. In this case, the expression for the angular velocity at time t would be:

ω = 6.5 rad/s + (6.5 rad/s² × 15 s) = 6.5 rad/s + 97.5 rad/s = 104.0 rad/s.

This equation shows that to find the final angular velocity, you simply add the product of the angular acceleration and time to the initial angular velocity. The units of angular velocity are in radians per second (rad/s).