10.2 Kinematics of Rotational Motion

Rotational kinematics has many useful relationships, often expressed in equation form. Are these relationships laws of physics or are they simply descriptive? (Hint: the same question applies to linear kinematics.)

With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s.

(a) What is its angular acceleration in rad/s²?

(b) How many revolutions does it go through in the process?

A gyroscope slows from an initial rate of 32.0 rad/s at a rate of $0 . \text{700} \textrm{ }\text{rad}/\text{s}^{2}$.

(a) How long does it take to come to rest?

(b) How many revolutions does it make before stopping?

Everyday application: Suppose a yo-yo has a center shaft that has a 0.250 cm radius and that its string is being pulled.

(a) If the string is stationary and the yo-yo accelerates away from it at a rate of $1 . \text{50} \textrm{ }\text{m}/\text{s}^{2}$, what is the angular acceleration of the yo-yo?

(b) What is the angular velocity after 0.750 s if it starts from rest?

(c) The outside radius of the yo-yo is 3.50 cm. What is the tangential acce…