Uniform circular motion of a rolling object

In summary, to find the number of revolutions of a soccer ball with a diameter of 33cm moving at a linear speed of 2.4m/s over a distance of 18m, you can use the equation N=X/2pi*r. However, be sure to use the correct value for the ball's radius in order to get an accurate answer.
  • #1
akatsafa
42
0
A soccer ball of diameter 33cm rolls without slipping at a linear speed of 2.4m/s. Through how many revolutions has the soccer ball turned as it moves a linear distance of 18m?

How do I just find the revolutions? I know how to use the equation to find rev/s, but how do I just get revolutions?

Thank you.
 
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  • #2
Find out how long it takes for the ball to do a full revolution. Then find out how long it takes for the ball to move 18 metres. Divide the latter by the former and you should get your answer.
 
  • #3
hint: there is superfluous information in the problem.
 
  • #4
I'm using the equation N=X/2pi*r. When I do this, I'm getting 8.68 revolutions, but it's wrong. Is there another equation I should be using?
 
  • #5
Nevermind. I know what I did wrong!
 
  • #6
akatsafa said:
I'm using the equation N=X/2pi*r. When I do this, I'm getting 8.68 revolutions, but it's wrong. Is there another equation I should be using?
Your equation is correct. Be sure you are using the correct value for the ball's radius.
 

FAQ: Uniform circular motion of a rolling object

What is uniform circular motion?

Uniform circular motion is the motion of an object moving along a circular path at a constant speed, where the direction of motion is constantly changing.

How is uniform circular motion different from linear motion?

In uniform circular motion, the speed of the object remains constant, but the direction of motion changes continuously. In linear motion, the speed and direction of motion remain constant.

What is the role of centripetal force in uniform circular motion?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is responsible for constantly changing the direction of motion in uniform circular motion.

How is angular velocity related to linear velocity in uniform circular motion?

Angular velocity is the rate of change of angular displacement, while linear velocity is the rate of change of linear displacement. In uniform circular motion, these two velocities are related by the formula v = rω, where v is linear velocity, r is the radius of the circle, and ω is the angular velocity.

What factors affect the speed of an object in uniform circular motion?

The speed of an object in uniform circular motion is affected by the radius of the circle, the mass of the object, and the centripetal force acting on the object. The greater the radius and/or the mass, the slower the object will move, while a larger centripetal force will result in a higher speed.

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