Chapter 8, Problem 52A

To determine

Whether the total acceleration of a point on the tire is inward, outward, tangential, or zero if it rotates at a constant rate of $14\text{rev/min}$ .

Answer to Problem 52A

Inward

Explanation of Solution

Introduction:

The constant rate of revolution of a toy means that it covers a fixed angular distance in a time.

If in a time, the point on a tire covers a fixed distance or undergoes fixed revolutions in a minute, then its angular velocity must be constant since the angular velocity is basically the time rate change of angular distance.

Now, if the angular velocity of the considered point is constant then its angular acceleration will be zero since angular acceleration is the time rate change of angular velocity.

But, when any object undergoes rotation, then centripetal force acts on it which is directed towards the axis of rotation of the object.

Thus, centripetal force, or thereby centripetal acceleration will act on a point on the tire which is towards the axis of the rotation of the tire, that is, towards the center of the tire.

Conclusion:

Hence, the total acceleration of a point on the tire, which is the sum of the angular and the centripetal acceleration, will be directed inwards, if it rotates at a constant rate of $14\text{rev/min}$ .