Question

Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located in the rim of the wheel and pint B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true?

1. The angular velocity at point A is greater than that of point B
2. Both points have the same centripetal acceleration
3. Both points have the same tangential acceleration4. Both points have the same instantaneous angular velocity
5. Each second, point A turns through a greater angle than point B

Answer 1

All points on a rotating wheel share the same instantaneous angular velocity; however, points farther from the axis will experience greater centripetal acceleration. The correct statement is that both points have the same instantaneous angular velocity.

Step-by-step explanation:

The question concerns the properties of points located at different radii of a rotating wheel, specifically relating to angular velocity, centripetal acceleration, and tangential acceleration. We can address the situation by considering the principles of circular motion. When a rigid wheel is rotating about a fixed axis, all points on the wheel have the same instantaneous angular velocity since every point on the wheel rotates through the same angle in the same amount of time.

Centripetal acceleration is proportional to the radius and the square of the angular velocity. Since point A, being at the rim, is farther from the axis than point B, point A experiences a greater centripetal acceleration. On the other hand, tangential acceleration is related to the angular acceleration and the radius. If the wheel is rotating with decreasing angular velocity, both point A and B experience the same tangential acceleration because it is a property of the wheel's rotation, not the points' individual locations.

The correct statement in this scenario is that both points have the same instantaneous angular velocity, which makes option 4 the true statement.

Answer 2

4. Both points have the same instantaneous angular velocity

Step-by-step explanation:

Angular velocity is a measure of the the number of rotations per unit time. This does not depend on the radius of the wheel. Hence, all points on the wheel have the same angular velocity. This invalidates option 1.

The centripetal acceleration is given by the product to the square of the angular velocity and the radius or distance from the centre. A and B are located at different distances from the centre. Hence, they have different centripetal acceleration. This invalidates option 2.

The tangential acceleration depends on the linear velocity which itself is a product of the angular velocity and the distance from the centre. Hence, it is different for both points because they are at different distances from the centre.

Since both A and B are fixed points on the wheel, they move through equal angles in the same time. In fact, for any other fixed point, they all move through the same angle in the same time. This invalidates option 5.