Ant's Path on Revolving Disc: Calculating Displacement and Path Length

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In summary, the conversation discusses an ant's position and movement on a Beatles record with a 14.80 cm radius. The question asks for the ant's path length and displacement. Attempts at solving the problem using various equations such as L=Rtheta, c^2=a^2+b^2, and s=rtheta are mentioned. Eventually, the correct solution is found by dividing the triangle into two right triangles and using the correct equation.
  • #1
omc1
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Homework Statement

An ant positioned on the very edge of a Beatles record that is 14.80 cm in radius revolves through an angle of 70.0o as the disk turns. What is the ant's path length?
What is the magnitude of the ant's displacement?



Homework Equations

L=Rtheta



The Attempt at a Solution


i was able to find the path length to 0.181 m and that's right but i can't find the displacement which seems like it should be easy...i used c^2=a^2+b^2 but that didnt work then i used costheta that didnt work so i used s=rtheta and that didnt work so ...please help, thanks
 
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  • #2
This gives you an isosceles triangle with two known sides and the angle between them also known ... how hard can it be ? Divide it into two right triangles and go from there.
 
  • #3
i did that and CAPA is still rejecting my answer...
 
  • #4
omc1 said:
i did that and CAPA is still rejecting my answer...

Why don't you write out, in full, one of your attempts so that we can see what might be going wrong?
 
  • #5
i did radius times tan35 equal the opposite leg then multiply by two ...207
 
  • #6
omc1 said:
i did radius times tan35 equal the opposite leg then multiply by two ...207

Ah, but I don't see that expression being correct. The radius is not the adjacent leg of the triangle.
 
  • #7
ic i found my mistake, thanks!
 

Related to Ant's Path on Revolving Disc: Calculating Displacement and Path Length

1. What is the concept of an ant on the edge of a disc?

The concept of an ant on the edge of a disc is a thought experiment used in physics to explain the concept of rotational motion and centripetal force. It involves imagining an ant walking on the edge of a spinning disc and how its motion would be affected.

2. How does the ant's motion on the edge of a disc relate to rotational motion?

The ant's motion on the edge of a disc is an example of rotational motion, as it is moving around a central axis. In this case, the ant is moving in a circular path due to the disc's rotation, and its velocity and acceleration are constantly changing as it moves along the curved path.

3. What is centripetal force and how does it apply to the ant on the edge of a disc?

Centripetal force is the force that acts towards the center of a circular path, keeping an object in circular motion. In the case of the ant on the edge of a disc, the centripetal force is provided by the friction between the ant's feet and the disc, allowing it to maintain its circular motion.

4. What factors affect the ant's motion on the edge of a disc?

The ant's motion on the edge of a disc is affected by several factors, including the disc's rotational speed, the ant's weight, and the coefficient of friction between the ant's feet and the disc's surface. These factors determine the magnitude and direction of the centripetal force acting on the ant.

5. How does the ant's motion on the edge of a disc illustrate the principles of angular velocity and acceleration?

The ant's motion on the edge of a disc demonstrates the principles of angular velocity and acceleration, as its velocity and acceleration are constantly changing as it moves along the curved path. The ant's angular velocity is directly proportional to the disc's rotational speed, while its angular acceleration is determined by the disc's rate of change in rotational speed.

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