# Circular Motion Path Length

1. Oct 6, 2010

### Jetsgirl

1. The problem statement, all variables and given/known data

An ant positioned on the very edge of a Beatles record that is 18.00 cm in radius revolves through an angle of 110.0o as the disk turns. What is the ant's path length?

What is the magnitude of the ant's displacement?

2. Relevant equations

Ac=v^2/r

T=2pir/v

3. The attempt at a solution

I'm really confused about this because if I don't have a velocity, how could I use any Circular Motion & Rotation equations to calculate the length?

I calculated v=(18 cm)(cos(110deg) = -17.98 (in radians) but I know this isn't right?

2. Oct 6, 2010

### JAK3CAL

also trying to solve this one.... im stumped

3. Oct 6, 2010

### kjohnson

It doesnt matter the angular speed. It's like saying you travel 10m at 5m/s how far did you travel?

All you need to know is the radius and the angle it rotates through.

There is a well known formula that relates arc length 's' to radius 'r' and angle 'a'...look that up and it will make quick work of this problem. You could also look at it like the circumference of a full circle is 2(pi)(r). So since the circle only rotates 110 degrees instead of 360 degrees simply set up a ratio of the total circumference to the arc length your trying to solve.

4. Oct 6, 2010

### Jetsgirl

Thanks so much, I got it!!

5. Oct 6, 2010

### JAK3CAL

as did i thank you!