# Tangential and radial accelereations of a flywheel

1. Feb 1, 2012

### 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.

arad = 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.

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

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

2. Feb 1, 2012

### tiny-tim

hi failexam!

all looks good

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

3. Feb 2, 2012

### 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).