Question about angular/linear velocity

[G1SG2]

I just wanted to make sure if I understand the difference. So, if we have some type of rotational motion (such as a merry-go-round):

1. a person standing on the edge would have a relatively greater tangential velocity than a person close to the center

2. but they both would have the same angular velocity

Right?

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[Chowdder]

You got it

 

[G1SG2]

thank you

this is because tangential velocity is dependent on r, but the angular velocity is dependent on the angle, right?

 

[Chowdder]

tangential velocity is dependent on how far you are from the centre of rotation. So yes it depends on r. Angular velocity depends on how fast the object is rotating. In other words, how much angle is the object rotating through per second. So it's value is dependent on the intrinsic speed of rotation.

 

[G1SG2]

tangential velocity is dependent on how far you are from the centre of rotation. So yes it depends on r. Angular velocity depends on how fast the object is rotating. In other words, how much angle is the object rotating through per second. So it's value is dependent on the intrinsic speed of rotation.

angular velocity w=v/r, so wouldn't that lead one to believe that angular velocity increases as r decreases, and that the person standing closer to the center has a larger angular velocity???

 

[Dr Gerrard]

That v in the equation is tangential velocity. As r increases in that, the v also increases.