# Velocity along an arc path

1. Jul 10, 2010

### rhill100

Hi everyone,

I started what I thought would be a simple algebra/trig problem and quickly learned that I was dead wrong. At least I think I am wrong. I need to determine how much the speed of a particle moving along an arc segment changes as the length of the distance to the center point changes if the angular velocity remains constant. I think I'm using the term angular velocity correctly..... My specific goal is to show mathematically to a couple of unbelieving friends that increasing the length of a golf shaft by 3 or 4 inches is not going to make as much of a difference in club speed as they believe it is. Assuming that two golf swings are exactly the same, how fast if the club head moving is the shaft is 44 inches long versus 48 inches long. What formula(s) should I be looking for? Does anyone know of a web site that may have some parametric functions on it that I could just plug in the numbers and see the difference? All I'm looking for is a percent of change between the two numbers. Thanks in advance, any guidance will be greatly appreciated.

Rob

2. Jul 10, 2010

### Sybren

the percentile velocity increase equals the precentile club length increase because

$$v=r\omega$$

3. Jul 11, 2010

### AJ Bentley

But you really need to worry about the energy stored in the swing, which is going to be proportional to v^2.

So the energy will go as the square of the club length.