# Constant Angular Velocity Problem

## Homework Statement

I encountered the following problem and I don't know where to begin or what formula to use... An object is moving in a circular path with a radius of 4.00 m. If the object moves through an arc length of 3.16m, then find the angular displacement?

I wish I knew.

## The Attempt at a Solution

Any help would be great thanks!

LowlyPion
Homework Helper
Welcome to PF.

What is the circumference of a circle with radius 4?

And what percentage of the circumference does 3.16 represent?

That percentage of 360° then ...

PhanthomJay
Homework Helper
Gold Member
Just look up (then study) the relationship between arc length (s), radius (r) and angular displacement (theta). Note that theta is in radians. If you have no textbook, try Google.

Welcome to PF.

What is the circumference of a circle with radius 4?

And what percentage of the circumference does 3.16 represent?

That percentage of 360° then ...

so I got the following figured out, circumerence is 25.13

to find the percentage of the circumference that 3.16 represents should I take 3.16/25.13? If so that number is .126, than what should I do with figuring out the percentage of 360°?

LowlyPion
Homework Helper
so I got the following figured out, circumerence is 25.13

to find the percentage of the circumference that 3.16 represents should I take 3.16/25.13? If so that number is .126, than what should I do with figuring out the percentage of 360°?

What you determined is the fraction of the circumference. Since there are 360 degrees in a full circle or alternatively there are 2*π radians in a circle ...

If you want degrees, then multiply by 360.

If you want it in radians, there are 2*π (2*3.1415), then multiply .126*6.283.

What you determined is the fraction of the circumference. Since there are 360 degrees in a full circle or alternatively there are 2*π radians in a circle ...

If you want degrees, then multiply by 360.

If you want it in radians, there are 2*π (2*3.1415), then multiply .126*6.283.

thanks thats what I needed to figure it out! Thanks