Suppose a record turntable rotates at constant angular velocity.

a) Does a point on the rim have radial and/or tangential acceleration?

b) If the turntable's angular velocity increases uniformly, does the point have radial and/or tangential acceleration?

c) For which cases would the magnitude of either of the components of linear acceleration change?

These questions are intended to get you to read the assignment and understand the two kinds of acceleration of rotating objects.

As long as it is rotating, a point that is not the center has some radial (centripetal) acceleration.

We will be glad to critique your thoughts.

a) When a record turntable rotates at a constant angular velocity, a point on the rim only has tangential acceleration. Radial acceleration is zero because the distance between the point and the center of rotation remains constant.

To understand this, we can use the concept of circular motion. In circular motion, an object with a constant speed moves in a circular path. The velocity vector of the object is always tangent to the circle, and its magnitude remains constant since the speed is constant.

Acceleration, on the other hand, is the rate of change of velocity. Tangential acceleration occurs when there is a change in the magnitude of velocity, even if the direction remains the same. In this case, the angular velocity of the turntable is constant, so the magnitude of the velocity does not change, resulting in zero tangential acceleration. However, the direction of the velocity continuously changes because it is tangent to the circular path.

b) If the turntable's angular velocity increases uniformly, the point on the rim will have both radial and tangential acceleration.

When the angular velocity increases uniformly, the object on the turntable experiences an increase in the magnitude of its velocity. Since the velocity vector is always tangent to the circular path, an increase in magnitude means there is a tangential acceleration. Additionally, as the angular velocity increases, the object moves farther from the center of rotation, resulting in a non-zero radial acceleration.

c) The magnitude of either of the components of linear acceleration will change when there is a change in the angular velocity of the turntable.

For example, if the angular velocity increases or decreases, the magnitude of the tangential acceleration will change because it depends on the rate of change of the velocity. Similarly, if the distance between the center of rotation and the point on the rim changes, such as when the object moves closer or farther away from the center, the magnitude of the radial acceleration will change.