- #1

Karol

- 1,380

- 22

## Homework Statement

A disk of radius R and mass m rotates on a floor with coefficient of friction μ and makes a circle of radius r

_{0}at constant speed v

_{0}.

What is the friction force between the disk and the floor.

What's the inclination angle α to the vertical.

It's suggested in the question to use cylindrical coordinate system in which ##\hat{r}## is from the center of the circle to the point of contact of the disk and ##\hat{\theta}## is in the tangential direction and ##\hat{z}## is upwards.

## Homework Equations

Centrifugal acceleration: ##a=\frac{v^2}{r}##

## The Attempt at a Solution

The friction force:

$$F=m\frac{v_0^2}{r_0}$$

The inclination angle. moments round point A=moments round the center o, but i am not sure i am allowed to choose 2 different points:

$$mgR\sin\alpha=m\frac{v_0^2}{r_0}R\cos\alpha\rightarrow \tan\alpha=\frac{v_0^2}{gr_0}$$

I don't understand why and how i have to use cylindrical coordinate system since i solved easily. i suspect it's incorrect.

If i want to take moments of both the friction force f and the weight round the same point i choose point B on the top but both forces rotate the disk counterclockwise.