Constant Angular Velocity Problem

AI Thread Summary
An object moving in a circular path with a radius of 4.00 m has an arc length of 3.16 m, prompting a discussion on how to calculate angular displacement. The circumference of the circle is determined to be approximately 25.13 m. To find the angular displacement, the fraction of the arc length to the circumference is calculated, yielding 0.126. This fraction can then be converted to degrees by multiplying by 360 or to radians by multiplying by 2π. The participants successfully clarify the relationship between arc length, radius, and angular displacement, leading to a solution.
math_girl
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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!
 
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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 ...
 
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.
 
LowlyPion said:
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°?
 
math_girl said:
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.
 
LowlyPion said:
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
 
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