# Circular motion

1. Nov 24, 2009

### songoku

1. The problem statement, all variables and given/known data
A grinding wheel has a diameter of 0.12 cm and spins horizontally at 1200 revolutions per minute about a vertical axis. A particle of mass 1 x 10-4 kg sticks to the wheel.

a. calculate the magnitude of the angular velocity, acceleration and force acting on the particle

b. the radial force that keeps the particle on the wheel is 2.5 N. calculate the angular velocity at which the particle leave the wheel.

c. if the wheel exceeds the angular speed in (b), calculate the speed and direction of motion of the particle just after it leaves the surface of the wheel.

2. Relevant equations
circular motion

3. The attempt at a solution
a.

$$\omega = 2\pi f = 2400\pi rad/s$$

$$a=\omega ^2 r = 14.4 \pi ms^2$$

$$F = ma = 1.44 x 10^{-3} \pi N$$

b.

$$F=m \omega ^2r$$

$$\omega ^2=\frac{2.5}{mr}$$

$$\omega= 2041.241 ~rad/s$$

c.

$$v=\omega r=12.247 ms^{-1}$$

Direction of motion : tangential to the point where it leaves

Do I get it right?

Thanks

2. Nov 24, 2009

### estalas

Assuming the particle is sticked to the very edge of the disk.

a) Check you angular velocity. the units is rad/s. and unit for the frequency is rev/min

3. Nov 24, 2009

### songoku

Hi estalas

Aah my bad, forgot to change the unit. how about (b) and (c)? Are they correct?

Thanks