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

In summary: This is because average velocity is calculated as the displacement divided by the elapsed time, and if the displacement is zero, the average velocity will also be zero. So for this problem, the average velocity over one revolution will be zero.
  • #1
dguilfoyle
1
0

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
 
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  • #2
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.
 

1. Did you use the correct kinematics equations?

It is important to use the correct kinematics equations for the given problem. Make sure you understand which equation relates to position, velocity, and acceleration.

2. Did you properly identify the known and unknown variables?

In kinematics problems, it is crucial to identify the known and unknown variables before solving. This will help you select the appropriate equation and solve for the desired variable.

3. Did you check for units and use the correct units in your calculations?

Make sure to check for units and use the correct units in your calculations. This will ensure that your final answer is in the correct units and is accurate.

4. Did you double-check your calculations for accuracy?

It is always a good idea to double-check your calculations to ensure accuracy. This will help catch any mistakes and provide confidence in your final answer.

5. Did you use proper sig figs in your final answer?

Be sure to use the correct number of significant figures in your final answer. This will help maintain the precision of your answer and avoid any rounding errors.

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