Angular and Linear Velocity Calculations

[Britannia]

Please could I have some help with the following question:

A driver wheel, which runs a drive belt has a diameter of 600mm and can run at a maximum speed of 750rpm. If the belt has a static coefficient of friction of 0.9 and a dynamic coefficient of friction of 0.87, calculate:

a) The angular velocity (Omega) of the wheel in rad/s.

b)The linear velocity of the wheel.

c) If the normal force between the belt and the driver wheel is 750N, what will be the maximum force which can be transmitted when the belt is running at a constant speed? Explain your answer.

d) If the speed of the wheel is reduced to 300rpm, over a period of 10s, calaulate the angular retardation.

Thanks for any help,

Chris

 

[Britannia]

This is what I got for a):

Omega1 = 750x2PI/60 = 78.53rad/s

 

[topsquark]

This is what I got for a):

Omega1 = 750x2PI/60 = 78.53rad/s

Good so far.

b) What is the relationship between linear speed and angular speed? I.e. do you know of a relationship between v and $$\omega$$?

c) I don't like the wording on this one. I'm assuming the question is talking about the force on the track being transmitted by the driver wheel because that's the only question we can answer. So, assuming the track is not slipping on the driver wheel the friction is static. We know the normal force and the coefficient of static friction...

d) Assume you know that the angular retardation is constant. (Or that you are finding the average angular retardation.) You know the change in angular speed, and you know how long it takes to do it. There are four equations that are typically used:
$$\theta=\theta_0+\omega_0t+(1/2)\alpha t^2$$
$$\theta=\theta_0+(1/2)(\omega_0+\omega )t$$
$$\omega=\omega_0+\alpha t$$
$$\omega^2=\omega_0^2+\alpha (\theta - \theta_0)$$
Which one looks useful?

-Dan