Tangential and radial accelereations of a flywheel

[spaghetti3451]

I found this question in a book and I am trying to answer it by myself. Here's the question and my solution.

A flywheel rotates with constant angular velocity. Does a point on its rim have a tangential acceleration? A radial acceleration? Are these accelerations constant in magnitude? In direction? In each case give the reasoning behind your answer.

The point on the rim of the flywheel is rotating in a circle. Therefore, the direction of its velocity is changing. Therefore, the point must have a radial acceleration.

The point is rotating with constant angular speed. Therefore, its linear speed is constant. Therefore, the point does not have a tangential acceleration.

a_rad = rω². In other words, the radial acceleration is a function of the radius of the circle and the angular speed of the point. Both are constant. So, the radial acceleration is constant in magnitude.

The point is rotating in a circle. Therefore, at each instant of time, the radial acceleration points from the particle to the centre of the circle. Therefore, as the particle rotates, the direction of the radial acceleration keeps changing.

a_tan = r$\alpha$. In other words, the tangential acceleration depends on the magnitude of the angular acceleration. This equals 0. Therefore, the tangential acceleration is non-existent in this case (as was shown before).



I would be grateful if you point out the flaws in my solution.

 

[tiny-tim]

hi failexam!

all looks good

(except you should have written |a_r|, and probably the last pargraph isn't necessary )

 

[Philip Wood]

Yes, an excellent answer. It would, I think, be good to have a vector diagram (of subtraction of velocities) to show why the acceleration is radial (paras 3 and 6).