Constant Angular Velocity Problem

[math_girl]

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?

Homework Equations

I wish I knew.

The Attempt at a Solution

Any help would be great thanks!

 

[LowlyPion]

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]

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.

 

[math_girl]

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]

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.

 

[math_girl]

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 that's what I needed to figure it out! Thanks