A DVD is rotating with an ever increasing speed. How do the angular velocity, an

Question

A DVD is rotating with an ever increasing speed. How do the angular velocity, angular acceleration, tangential velocity, and tangential acceleration compare at points P and Q? Angular velocity, angular acceleration, tangential velocity, and tangential acceleration are larger for point Q than for point P. 0 Points P and Q have the same angular velocity but point Q has a larger angular acceleration. Points P and Q have the same angular velocity and the same angular acceleration. Point Q has a larger tangential acceleration but points P and Q have the same tangential velocity. Points P and Q have the same tangential velocity and the same tangential acceleration.

Explanation / Answer

here

The angular velocity and angular acceleration must apply to all points on a rotating disk. For example, if any one point undergoes ¼ rotation, then ALL points must have undergone ¼ rotation. After that is obvious, then it is easy to conclude that if any point is changing its angular velocity at a given rate, then ALL points must be changing their angular velocity at the same rate. Conclusion: the angular acceleration at P and Q must be the same.

We have two more accelerations that can be considered for a point on a rotating disk: the tangential acceleration (a_tan) and the radial (or "centripetal") acceleration (a_rad). The formula for these are
a_tan = * r
where r is the distance of the point from the axis of rotation, and
a_rad = ² * r

As you can see, both of these quantities depend on the radius of rotation, and both vary linearly with it. All points with a greater radius than point P must necessarily have greater tangential and radial accelerations.
so the correct answer is A

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