How Do You Calculate Linear Acceleration from Wheel Diameter and RPM Changes?

[icg]

Hey everyone, first time poster here It's a really great forum though!

I can't seem to figure out this problem. If anyone could help that would be great.


1.A bicycle has wheels with a diameter of 0.650 m. It accelerates uniformly and the rate of rotation of its wheels increases from 177rpm to 275rpm in a time of 18.5 s. Find the linear acceleration of the bicycle.


I converted rpm to rad/s, and then found angular acceleration using a=vf-vi/t, but how do you find the linear acceleration given the diameter.


And there's also this one:

2.The tires of a car make 78.0 revolutions as the car reduces its speed uniformly from 92.5 km/hr to 55.9 km/hr. The tires have a diameter of 0.908 m. What was the angular acceleration?

 

[OlderDan]

If you start with the definition of an angle as the ratio of arc length to radius, you see that the distance the center of a wheel moves when roilling without slipping is proportional to its angular displacement (rotation in radians). It follows that linear velocity is proportional to angular velocity and linear acceleration is probportional to angular acceleration. Can you come up with these relationships?

 

[Pseudo Statistic]

The radius is half the diameter, isn't it? ;)