Small Circular Acceleratioon Question

[LadyMario]

A wheel of 0.50 m radius rotates at 15 rev/s. What is the acceleration at its outer rim in m/s²

They want tangential acceleration right? Is there anyway to solve this without angular velocity/speed as we haven't learned that yet. This is part of the practice questions for my midterm on Work/Energy and Kinematics, so I'm looking for one of those methods to solve it.

The answer is 4.4x10³ m/s² but I can't seem to get that. Help?

 

[lewando]

What did you get and how did you get it?

 

[LadyMario]

I was using T=2piR/V to get V and then using that in a=V^2/R but a friend pointed out the 15 rev/s is frequency, and so I'm not sure of an equation for that.

 

[lewando]

T = 1/f. If the frequency is 15 revolutions/s, how many seconds would it take for 1 revolution? Your formula for acceleration is for radial acceleration, not tangential. Since the answer is non-zero, question refers to radial.

 

[LadyMario]

Yes I get that frequency means it will be 1/15 but what equation can I use to get tangential?

 

[lewando]

a_tangential = dV/dt.

 

[LadyMario]

a_tangential = dV/dt.

oh okay. I was thinking about how to get that equation, how do I get time and velocity though? From the Period equation: T=2piR/V but this time T= 1/15 and solve for V?

 

[lewando]

Not sure if you are on the right track per your tangential acceleration inquiry. V can be found from the period equation. You are looking for a_radial.