# What is the relationship between radius and tangential velocity?

So imagine you had a tennis racket. Let's say it is 27 inches. The swinger will swing the racket and at the tip of the racket it's going a certain speed.

If we increased the length of the racket to 29 inches, is the increase of speed at the tip linear or is it exponential?

Thanks for the help guys, this wasn't a homework question btw, i was just curious.

• Are you more interested in the speed of the racket or of the ball? First google result that might be helpful was this.
– Nat
May 29 '18 at 6:40
• i assumed the speed at the tip of the racket = the ball right? But someone already answered it as linear thanks May 29 '18 at 6:43
• If you can keep the angular velocity same somehow then the velocity increases linearly with radius. (v = rw) May 29 '18 at 6:56

$$v = \omega r$$
where $\omega$ is the angular velocity.