How Do You Calculate Path Length and Displacement on a Circular Track?

[Jetsgirl]

Homework Statement

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?

Homework Equations

Ac=v^2/r

T=2pir/v

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?

 

[JAK3CAL]

Homework Statement

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?

Homework Equations

Ac=v^2/r

T=2pir/v

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?

also trying to solve this one... I am stumped

 

[kjohnson]

It doesn't 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.

 

[Jetsgirl]

Thanks so much, I got it!

 

[JAK3CAL]

Thanks so much, I got it!

as did i thank you!