10.1 Rotational Variables

A clock is mounted on the wall. As you look at it, what is the direction of the angular velocity vector of the second hand?

A baseball bat is swung. Do all points on the bat have the same angular velocity? The same tangential speed?

A track star runs a 400-m race on a 400-m circular track in 45 s. What is his angular velocity assuming a constant speed?

A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?

Unreasonable results. The propeller of an aircraft is spinning at 10 rev/s when the pilot shuts off the engine. The propeller reduces its angular velocity at a constant $2.0 \text{rad} / \text{s}^{2}$ for a time period of 40 s. What is the rotation rate of the propeller in 40 s? Is this a reasonable situation?

On takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular velocity for 3.0 s from rest at a rate of $\omega = \left(25.0 t\right) \text{rad} / \text{s}$ where t is measured in seconds. (a) What is the instantaneous angular velocity of the propellers at $t = 2.0 \text{s}$? (b) What is the angular acceleration?