I need explained answers A small piece of clay is stuck near the edge of a phono

Question

I need explained answers A small piece of clay is stuck near the edge of a phonograph turntable. Let alpha vector represent the angular acceleration of the clay and a vector, represent the centripetal acceleration of the clay. a. For each situation described below, describe a possible motion of the turntable. (Some parts have more than one correct answer.) Explain your reasoning in each case. i. |alpha vector| = 0 and |a vector_r| = 0 ii. |alpha vector| = 0 and |a vector_r| notequalto 0 iii. |alpha vector| notequalto 0 and |a vector_r| notequalto 0 b. The equation "alpha vector = a vector_r/r" is not a correct vector equation. i. Explain how you can tell that the vector equation above is not correct.

Explanation / Answer

i.) The turntable is not turning. There is no motion. Otherwise, with no centripetal acceleration, the clay would not stay on the turntable.

ii.) The turntable is turning at a constant, non-zero angular velocity. The rate at which the turntable turns does not change.

iii.) The turntable is turning at an increasing or decreasing, non-zero angular velocity.


Angular acceleration is the rate of change in the angular velocity. In other words, it's how fast the rate of rotation is increasing or decreasing.

Centripetal acceleration is necessary for circular motion to exist because of inertia. Since objects in motion want to remain in motion at the same speed in a straight line, a force that is perpendicular to this straight line must be continuously applied to an object to keep it in circular motion. At any point on a circular path, an object wants to continue with its current instantaneous velocity in a line tangent to its current position on the circular path. Therefore, the direction of the perpendicular force (centripetal force) and centripetal acceleration are continuously changing. Since acceleration is the rate of change in velocity, all it takes is for the direction of the velocity to change in order for there to be a non-zero acceleration. What makes it centripetal acceleration is that it is pointing toward the center of the circular path and is a result of the centripetal force keeping the object on that path.

If there is an object in circular motion, it has non-zero centripetal acceleration and vice-versa.

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