Chapter 8, Problem 22Q

To determine

a)The direction of the linear velocity of a point on the top of the rotating wheel

b)The direction of the tangential linear acceleration of this point

c)If the angular speed is increasing or decreasing

Answer to Problem 22Q

Solution:

a)At the top of the rotating wheel the direction of the linear velocity of a point is south

b)At this point the direction of the tangential linear acceleration is south

c)The angular speed will be decreased.

Explanation of Solution

a)The right hand rule can be used to find the direction of linear velocity. If the thumb points in the direction of angular velocity, i.e. west, the fingers towards the top of the right palm curl towards the north. Thus, the linear velocity at the top of the rotating wheel is directed towards the north.

b)If the angular acceleration points towards the east, this means that change in the angular velocity points towards the east. Again using the right hand rule, the thumb now points towards the east, with the fingers at the top curling towards the south. Thus, a change in linear velocity is directed towards the south, and hence tangential linear acceleration is directed towards the south.

c)Since the angular acceleration is in a direction opposite to that of angular speed, the angular speed is decreasing.