Question

A disk with an initial angular velocity Ω0 = 6.5 rad/s experiences a constant angular acceleration of α = 9.5 rad/s2 for a time period t = 15 s. What is the final angular velocity of the disk?

1) Ω = Ω0 + αt
2) Ω = Ω0 + αt²
3) Ω = αt
4) Ω = Ω0t + 0.5αt²

Answer 1

The final angular velocity of the disk is calculated to be 149 rad/s after applying the rotational kinematics equation.

Step-by-step explanation:

The final angular velocity of the disk can be computed using the kinematic equation for rotational motion: Ω = Ω0 + αt. This equation relates the final angular velocity (Ω) to the initial angular velocity (Ω0), the angular acceleration (α) and the time interval (t).

In this case, the initial angular velocity (Ω0) is given as 6.5 rad/s, the constant angular acceleration (α) as 9.5 rad/s2, and the time interval (t) as 15 s. Plugging these values into the equation results in:

Ω = 6.5 rad/s + (9.5 rad/s2 * 15 s) = 6.5 rad/s + 142.5 rad/s = 149 rad/s.

Therefore, the final angular velocity of the disk is 149 rad/s.