Need help with a kinematics problem. I'm not sure if I did it properly.

[dguilfoyle]

Homework Statement

6) a helicopter blade spins at exactly 100 revolutions per minute. It's tip is 5.00m from the center of it's rotation. (a) calculate the average speed of the blade tip from the helicopters frame of reference. (b) What is it's average velocity over one revolution?

radius of rotation = 5.00m
100 revolutions per minute

Homework Equations

a) Average speed = total distance traveled/elapsed time
b) Average Velocity = Δx/Δt = (Xf - Xo)/t

The Attempt at a Solution

a) distance traveled = circumference of rotation
C = ∏d = 31.4m
time elapsed during one rotation = 60s/100 revolutions = 0.6 s/revolution
Therefore each revolution takes 0.6s and the elapsed time would be 0.6s

Average speed = 31.4m/0.6s/revolution = 52.3 m/s/revolution.
I interpret this to mean that the average speed of one revolution is 52.3m/s. Is that the correct way to interpret this result? Is this result even correct? Did I go wrong in my operations?

b) Average velocity = Δx/Δt = 0/0.6s - 0 = 0
I don't think I did this part correctly at all. But if it is a revolution, and this question is based on one revolution, then displacement would be zero, right? you would end up back at the same spot.

Any help would be appreciated.
Thanks

 

[TSny]

Welcome to PhysicsForums, dguilfoyle!

Your work looks very good. The average speed for the whole 100 revolutions is 52.3 m/s. If the blade is spinning at a constant rate, then the tip would be moving with a constant speed of 52.3 m/s and so the average speed over one revolution or any other number of revolutions would also be 52.3 m/s.

You're right also regarding the average velocity. Whenever the overall displacement is zero, the average velocity will be zero.