Kinetic Energy of a Rolling Ball on a Horizontal Plane

In summary, to find the kinetic energy of a uniform ball or mass rolling without slipping on a horizontal plane and moving along a circular path of radius R, you must consider both the translational and rotational kinetic energy. The translational kinetic energy is equal to half the mass times the velocity squared, while the rotational kinetic energy is equal to half the moment of inertia times the angular velocity squared. Since the ball is also rotating about a vertical axis, you must add the rotational kinetic energy around the center of the circle to the total kinetic energy.
  • #1
ChuckNorris
1
0

Homework Statement



Uniform ball or mass m and radius r rolls on a horizontal plane without sipping, at the same time moving along a circular path of radius R. Speed of the center of mass is constant and equals v. Find it's kinetic energy.

Homework Equations



I=2/5 m r^2

The Attempt at a Solution



KE of ball's translation T1=(m v^2)/2

KE of ball's rotation T2=(I w^2)/2 ( w - angular velocity, from w r = v => w= v/r)

My problem is with the ball moving along a circle of radius R. Where does it come into play?
Do i have to add the KE of ball rotation around the center of the circle?

Any help will be appreciated.
 
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  • #2
The ball is also rotating about a vertical axis as it moves in the circle.
 

Related to Kinetic Energy of a Rolling Ball on a Horizontal Plane

1. What is the kinetic energy of a ball rolling in a plane?

The kinetic energy of a ball rolling in a plane is the energy that it possesses due to its motion. It is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the ball and v is its velocity.

2. How does the mass of the ball affect its kinetic energy?

The mass of the ball directly affects its kinetic energy. The greater the mass of the ball, the greater its kinetic energy will be, as seen in the formula KE = 1/2 * m * v^2. This means that a heavier ball rolling in a plane will have more kinetic energy than a lighter ball with the same velocity.

3. What is the relationship between the velocity and kinetic energy of a ball rolling in a plane?

The relationship between the velocity and kinetic energy of a ball rolling in a plane is directly proportional. This means that as the velocity of the ball increases, its kinetic energy also increases. Conversely, as the velocity decreases, the kinetic energy also decreases.

4. Can the kinetic energy of a ball rolling in a plane be negative?

No, the kinetic energy of a ball rolling in a plane cannot be negative. This is because kinetic energy is a measure of the energy possessed by an object due to its motion, and motion cannot have a negative value. However, the velocity of the ball can be negative, which would result in a negative value for kinetic energy, but this would indicate that the ball is moving in the opposite direction.

5. How does the height of the plane affect the kinetic energy of a rolling ball?

The height of the plane does not have a direct effect on the kinetic energy of a rolling ball. However, if the plane has a slope, the height will affect the potential energy of the ball, which can then be converted into kinetic energy as the ball rolls down the slope. In this case, the higher the plane, the greater the potential energy, and therefore the greater the kinetic energy as the ball rolls down the slope.

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