How Does Roughness Affect the Time Period of a Ball Rolling on a Vertical Hoop?

In summary, when a ball is rolling on a rough vertical hoop with its lowest point being the mean position and undergoing to and fro motion with small angular displacement, the time period is dependent on factors such as the radius, gravitational force, and angular displacement. This is determined using rotational motion equations where the torque provided by the gravitational force is about the center of the hoop and not the lowest point in contact with the ground. The reaction force at this point does not contribute to the torque and the point of rotation is the center of the hoop.
  • #1
Bilbo B
9
1
Homework Statement
Finding the time period dependence upon another factors such as (radius, g, angular displacement) of the ball.
Relevant Equations
torque balance equation
If the ball's rolling on a vertical hoop placed in contact with floor and with the lowest point being the mean position of the ball undergoing to and fro motion with small angular displacement. In what ways it's time period is solved out provided the surface of the hoop is rough.
If the block is in mean position then the total gravitational force is balanced out with the reaction force.
But when it is displaced with small angle, let theta the gravitational force provides torque about the center of hoop and not about the lowest point which is in contact with the ground then such it depends upon the angle. The problem is the reaction force at this point has nothing to do with providing torque and point about which it rotates is the center of hoop.
 
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  • #2
Bilbo B said:
Homework Statement:: Finding the time period dependence upon another factors such as (radius, g, angular displacement) of the ball.
Relevant Equations:: Using rotational motion mechanism

If the ball's rolling on a vertical hoop placed in contact with floor and with the lowest point being the mean position of the ball undergoing to and fro motion with small angular displacement. In what ways it's time period is solved out provided the surface of the hoop is rough.
Welcome to the PF. :smile:

You must show the Relevant Equations and post your work before we can be of tutorial help. Please reply with that information, and we will try to make sure that you are not leaving anything out of your work. Thanks.
 

FAQ: How Does Roughness Affect the Time Period of a Ball Rolling on a Vertical Hoop?

1. How does the ball stay on the hoop while rolling?

The ball stays on the hoop due to the combination of inertia and centripetal force. Inertia is the tendency of an object to maintain its state of motion, while centripetal force is the force that acts towards the center of a circular motion. As the ball rolls along the hoop, the centripetal force provided by the hoop keeps the ball moving in a circular motion, preventing it from flying off.

2. What factors affect the speed of the ball while rolling along a hoop?

The speed of the ball while rolling along a hoop is affected by several factors, including the mass of the ball, the diameter of the hoop, and the force applied to the ball. A heavier ball will require more force to maintain its speed, while a larger hoop will allow for a higher speed. Additionally, the friction between the ball and the hoop can also affect the speed.

3. Can the ball roll along the hoop forever?

In theory, yes, the ball can roll along the hoop forever if there is no external force acting on it. This is because of the principle of conservation of energy, which states that energy can neither be created nor destroyed, only transferred from one form to another. As long as there is no friction or other external forces, the ball will continue to roll along the hoop with the same speed and energy.

4. How does the shape of the hoop affect the ball's motion?

The shape of the hoop can affect the ball's motion in several ways. A circular hoop will provide a smooth and consistent path for the ball to roll along, while a square or triangular hoop may cause the ball to bounce or change direction. Additionally, the curvature of the hoop can also impact the speed and direction of the ball.

5. What happens if the ball is released from a higher point on the hoop?

If the ball is released from a higher point on the hoop, it will have more potential energy due to its increased height. As it rolls down the hoop, this potential energy will be converted into kinetic energy, causing the ball to roll faster. However, if the hoop is not perfectly circular, the ball may also experience changes in direction as it rolls down the hoop.

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