Circular Motion Homework: Angular Velocity, Acceleration, Force Calculation

[songoku]

Homework Statement

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.

Homework Equations

circular motion

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 leavesDo I get it right?

Thanks

 

[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

 

[songoku]

Hi estalas

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

Thanks