Rotational Motion Quick Concept help

[imbackasd]

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So for rotational motion the formula for angular velocity is angular displacment over time right?

Thus for this example:

A fly is sitting on the edge of a record with a radius of 0.2m spinning at constant velocity. If the fly completes 6 revolutions in 30s, what is the angular velocity of the record? What is the translational velocity of the fly?


Shouldnt the angular displacment be 0 since a singe roation puts you back in the same position and displacement is a change in position?

 

[johnnybravo19]

circumfrence is 2pi(r)
so 6.3*0.2m would be 1.26 m

and divide that by 5s since 30s/6=5s
you would get 0.25m/s

 

[imbackasd]

I understand the answer but my question is conceptionally why is angular displacement (6 * 2pi r) instead of 0 since displacement is change in position and a revolution lands you back in the same place you started at?

 

[johnnybravo19]

The answer is that it all comes down to mathematical approach. The displacement in this case is the relationship between the distance around the circle AND distance from the center of the circle.

Just memorize this as an exception, because how it's derived is not important and can be seen as a waste of time in scope of the MCAT. Put it on a flash card or something.

 

[V5RED]

I understand the answer but my question is conceptionally why is angular displacement (6 * 2pi r) instead of 0 since displacement is change in position and a revolution lands you back in the same place you started at?

Translational motion and angular motion are not the same thing.

In translational terms, the fly has a zero average displacement and a zero average velocity since the sum of its displacements is zero and the sum of its velocities is also zero.(edit: it does have an instantaneous velocity of magnitude equal to its speed)

In rotational terms, the fly has a displacement because its angular velocity is a constant. Angular motion is either clockwise or counterclockwise and the fly never changes direction. If you want a visual, imagine unwinding a spool of thread. As the spool rotates, the string gets longer because there is a constant angular velocity leading to more and more displacement.

 

[V5RED]

The answer is that it all comes down to mathematical approach. The displacement in this case is the relationship between the distance around the circle AND distance from the center of the circle.

Just memorize this as an exception, because how it's derived is not important and can be seen as a waste of time in scope of the MCAT. Put it on a flash card or something.

OP is asking about angular displacement. This has nothing to do with distance from the center of the circle. On a disc of 100 meter radius that is rotating, the angular displacement of a point near the center is the same as the angular displacement of a point on its edge.