Question

A blu-ray disc rotates counterclockwise and speeds up at a constant rate. how does the tangential acceleration of point p compare to the tangential acceleration of point q?

Answer 1

The figure of the problem is missing.

However, we can solve it this way. First of all, every point of the disk has the same angular acceleration, which is the rate of variation of the angular velocity in time. In fact, the disk rotates coherently, therefore all the points cover the same angle during the same time interval.

Then, the tangential acceleration of a generic point on the disk is related to the angular acceleration
`\alpha` by the following relation:

`a_(tan) = \alpha r`
where r is the distance of the point from the center of the disk.

Therefore, if we call
`r_P` the distance of point P from the center and
`r_Q` the distance of point Q from the center, we can find the ratio of the tangential accelerations between the two points:

`\frac{a_(tanP)}{a{tanQ}} = (r_P \alpha)/(r_Q \alpha) = (r_P)/(r_Q)`

So, the larger is the distance of the point from the center, the larger is the tangential acceleration.