rubber wheel (angular acceleration)

FossilFew

A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 2.0cm and accelerates at the rate of 7.2rad/s^2 and it is in contact with the pottery wheel (radius 25.0cm) without slipping. Calculate:
a) the angular acceleration of the pottery wheel
b) the time it takes the pottery wheel to reach its required speed of 65rpm


My approach:
What I can determine with the rubber wheel:

0.02m = r
7.2 rad/s^2 = angular acc

Atan= (0.02)(7.2) = .144 m/s^2

I think the Atan is the radial acceleration for the pottery wheel but I'm not sure.
If I can get the angular acceleration I can solve for t using Wot + 1/2 (angular acceleration) t^2 = theta ( I think).

If I assumed Atan was the radial acceleration I attempted to solve for w in Radial Acceleration= w^2r w = 0.76m/s

I'm not sure what to think of my approach. The key is what type of acceleration is transferred from the rubber wheel to the pottery wheel?

Thanks in advance. This forum is great!

OlderDan

The angular displacement of the big wheel is proportional to the angular displacement of the small wheel. That means the angular velocities and accelerations are also proportional with the same ratio. How many radians does the big wheel rotate when the small wheel rotates one radian?

FossilFew

So R2 is 12.5 times the radius of the rubber wheel. This means that the angular acceleration of the second wheel is 1/12.5 the given angular acceleration of the rubber wheel? This also means the torque on the second wheel is 12.5 times the torque on the rubber wheel?

Does this sound correct?

Thanks.

OlderDan

Your conclusion about the torque applies only to the magnitudes of the torques the wheels exert on one another. By Newton's third law they must apply equal and opposite forces upon one another, so the torques would be in proportion to their radii. The net rorque on the small wheel includes some driving torque from a motor that has to overcome the torque from the big wheel to accelerate the small wheel. You would need to know the moments of inertia of both wheels to analyze the torques in the problem. You do not have this information. Fortunately, you do not need it. This prolem is not about the torques on the wheels.