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

AI Thread Summary
To calculate the path length of an ant on a circular track with an 18 cm radius that revolves through an angle of 110 degrees, one can use the formula for arc length, which relates the radius and the angle in radians. The arc length can be determined by converting the angle from degrees to radians and applying the formula s = r * a, where 's' is the arc length, 'r' is the radius, and 'a' is the angle in radians. Displacement, on the other hand, is the straight-line distance from the starting point to the ending point, which can be calculated using the radius and the angle. The discussion emphasizes that velocity is not necessary for these calculations, as only the radius and angle are required. Understanding these concepts allows for straightforward solutions to the problem.
Jetsgirl
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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?
 
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Jetsgirl said:

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
 
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.
 
Thanks so much, I got it!
 
Jetsgirl said:
Thanks so much, I got it!

as did i thank you!
 

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