Tangential Velocity Question

[discowisco]

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How long will a person on a circular track take to complete one lap, if the radius of the track is 1000m and they have a tangential speed of 3 m/s?

A) (2pi x 1000) / 3


The answer was A.

Now the explanation in BR is distance / rate which is 2pir/ velocity however what I used was:

2pi / angular velocity .... which still comes out to the right answer.

However, why can you use tangential velocity to solve it like BR did, since dont you have to use angular velocity since it is a circular rotation type of problem?

 

[Deadlifts]

How long will a person on a circular track take to complete one lap, if the radius of the track is 1000m and they have a tangential speed of 3 m/s?

A) (2pi x 1000) / 3


The answer was A.

Now the explanation in BR is distance / rate which is 2pir/ velocity however what I used was:

2pi / angular velocity .... which still comes out to the right answer.

However, why can you use tangential velocity to solve it like BR did, since dont you have to use angular velocity since it is a circular rotation type of problem?

What is the relationship between angular velocity (omega) and tangential velocity?

omega = tangential velocity / r

so 1/omega = r/v.