Question

you are told that a basketball player spins the ball with an angular acceleration of 113 rad/s².
(a) what is the balls final angular velocity (in rad/s) if the ball starts from rest and the acceleration lasts 1.70 s?
rad/s
(b) what is unreasonable about the result?

this answer has not been graded yet.
(c) which premises are unreasonable or inconsistent?

Explanation:

Step1: Use the angular velocity formula

The formula for angular velocity is \(\omega=\omega_{0}+\alpha t\). Given \(\omega_{0} = 0\) (starts from rest), \(\alpha=113\ rad/s^{2}\), and \(t = 1.70\ s\).

Step2: Substitute the values

Substitute the values into the formula: \(\omega=0+(113\ rad/s^{2})\times(1.70\ s)\)

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For part (b), a basketball spinning at \(192.1\ rad/s\) is extremely fast. In reality, basketballs spun by players have much lower angular velocities. For part (c), the angular acceleration value of \(113\ rad/s^{2}\) is likely too high for a basketball being spun by a player.

Answer:

a. \(192.1\ rad/s\)
b. The angular velocity is extremely high for a basketball spun by a player.
c. The value of the angular acceleration (\(113\ rad/s^{2}\)) is unreasonable for a basketball being spun by a player.