Question

You are told that a basketball player spins the ball on his finger with an angular acceleration of 91 rad/s^2. What is the angular velocity of the ball?

a) 45.5 rad/s
b) 91 rad/s
c) 182 rad/s
d) 273 rad/s

Answer 1

The angular velocity of the ball is 182 rad/s. The correct answer is c) 182 rad/s.

Step-by-step explanation:

The angular acceleration of the basketball player spinning the ball is given as 91 rad/s². To determine the angular velocity, we can use the equation:

ω^2 = ω_0^2 + 2αθ

Where ω is the final angular velocity, ω_0 is the initial angular velocity, α is the angular acceleration, and θ is the angle covered. Since the basketball player spins the ball from rest, the initial angular velocity is zero. The angle covered can be calculated using the equation:

θ = (1/2)α t^2

Substituting the given values, we find that the final angular velocity of the ball is 182 rad/s. Therefore, the correct answer is (c) 182 rad/s.