Ring c has an inside radius of 55 mm and an outside radius of 60 mm and is positioned between two wheels a and b, each of 24-mm outside radius. knowing that wheel a rotates with a constant angular velocity of 300 rpm and that no slipping occurs, determine (a) the angular velocity of the ring c and of wheel b, (b) the acceleration of the points on a and b that are in contact with c.

a)

b)

Where is the acceleration of a point on the outer rim of wheel A and the acceleration of a point on the outer rim of wheel B.

Explanation:

a)

Because there are no specification on what units we should give the answer it would be educational to give the answer in both ways, rpm and rad/s.

Attached is a sketch of the situation.

Let's define the following variables:

Wheel A rotates with an angular velocity of

Reminding that the linear velocity is related to the angular velocity by where is the radius of the circular motion, we can determine the angular velocity of wheel B.

At point of contact 1 we have the same linear velocity for the outer radius of wheel A as the outer radius of wheel C. Thus we have:

Now we move to point of contact 2:

alternatively we can express this as rad/s per second by doing:

b)

The acceleration of a point undergoing circular motion is

Thus for a point in the outer rim of A we have and .

We obtain from the previous

Similarly: