# Why does the ball need to be rotating before colliding with the surface to skid?

• Game_Of_Physics
In summary, the conversation discusses the problem of a spherical ball colliding with a rigid surface at an angle, assuming the ball skids during the collision. It is mentioned that the solution to this problem claims that the ball cannot skid if it is not rotating prior to colliding with the surface. However, this claim is false and the error is considered cosmetic and does not affect the solution. The important factor is the force of friction between the ball and surface, which is given by the normal force multiplied by the coefficient of kinetic friction.
Game_Of_Physics
An elastic spherical ball of mass m and radius a moving with velocity v strikes a rigid surface at an angle θ to the normal. Assuming the ball skids while in contact with the surface, the tangential reaction force being a constant fraction μ of the normal reaction force, and assuming the perpendicular velocity of the ball is reversed, show that
1. the ball is reflected at an angle Φ to the normal where |tanθ - tanΦ| = 2μ
2. the angular velocity of the ball changes by an amount 5μvcosθ/a

Now the solution I have for this says that the ball can't skid if it is not rotating prior to colliding with the surface. I don't understand why this has to be the case. Could someone help explain why this is?

Thanks

Game_Of_Physics said:
Now the solution I have for this says that the ball can't skid if it is not rotating prior to colliding with the surface. I don't understand why this has to be the case.
So the claim is that if a ball is hitting the surface at a non-perpendicular angle and if it is not rotating as it arrives, then it cannot skid.

That claim is obviously false. Take the limiting case of a glancing impact at an angle of 89+ degrees from the normal with a greased ball. The ball will darned sure skid.

That's what it says, and as you suggest, this seems very counter-intuitive. The solution is from a book by a Cambridge professor though so I was reluctant to question it. Could it be a mistake?

Game_Of_Physics said:
That's what it says, and as you suggest, this seems very counter-intuitive. The solution is from a book by a Cambridge professor though so I was reluctant to question it. Could it be a mistake?
Mistake or misinterpretation. It is difficult to say without seeing the exact claim in context.

jbriggs444 said:
Mistake or misinterpretation. It is difficult to say without seeing the exact claim in context.

Here is the quote from the book:

"The problem refers to a change in angular velocity of the ball, so it is presumably not safe to assume that the ball is not initially rotating (and in fact if the ball were not rotating, it could not skid against the surface so the angles θ and Φ would be identical)."

Game_Of_Physics said:
Here is the quote from the book:

"The problem refers to a change in angular velocity of the ball, so it is presumably not safe to assume that the ball is not initially rotating (and in fact if the ball were not rotating, it could not skid against the surface so the angles θ and Φ would be identical)."
That claim is indeed incorrect and confused. The author of that quote could be correct to point out that a ball with an inadequate rotation rate might start the collision in a skidding condition and end the collision in a rolling-without-slipping condition. But the problem poser ruled that possibility out with the careful phrasing:
Game_Of_Physics said:
Assuming the ball skids while in contact with the surface
However, the error is cosmetic. It does not change the solution.

Whether one assumes that the ball starts with sufficient back spin that the skid persists throughout the collision or whether one assumes that the collision is at a sufficiently glancing angle it's still skidding when it rebounds, the important thing is that the force of friction between ball and surface persists throughout the collision and is given by the normal force multiplied by the coefficient of kinetic friction.

jbriggs444 said:
That claim is indeed incorrect and confused. The author of that quote could be correct to point out that a ball with an inadequate rotation rate might start the collision in a skidding condition and end the collision in a rolling-without-slipping condition. But the problem poser ruled that possibility out with the careful phrasing:

However, the error is cosmetic. It does not change the solution.

Whether one assumes that the ball starts with sufficient back spin that the skid persists throughout the collision or whether one assumes that the collision is at a sufficiently glancing angle it's still skidding when it rebounds, the important thing is that the force of friction between ball and surface persists throughout the collision and is given by the normal force multiplied by the coefficient of kinetic friction.

Thanks! And if the question had not said to assume that the ball slips during the collision, how would one go about solving the subsequent motion of the ball? If it doesn't slip during the collision, does that mean it no longer receives an impulse parallel to the wall? Would you be able to conserve kinetic energy in that circumstance?

Game_Of_Physics said:
Thanks! And if the question had not said to assume that the ball slips during the collision, how would one go about solving the subsequent motion of the ball? If it doesn't slip during the collision, does that mean it no longer receives an impulse parallel to the wall? Would you be able to conserve kinetic energy in that circumstance?
One would need additional details on the collision and the ball. For instance, the elasticity of the ball could figure in.

If you have ever bounced a sticky rubber ball (do they still make "superballs"?), you will understand that spin makes a huge difference in rebound angle for a ball that rebounds elastically and without slipping.

Just because the ball does not slip does not mean that there is no friction. Nor does it mean that there is no energy loss.

Looks to me like the writer got lost in a grammatical loop of too many "nots".

Game_Of_Physics and jbriggs444

## 1. How does the angle of impact affect the rebound of a ball off a wall?

The angle of impact plays a significant role in the rebound of a ball off a wall. If the ball hits the wall at a perpendicular angle, it will bounce back in the opposite direction with the same speed. However, if the angle of impact is not perpendicular, the ball will rebound at a different angle and with a different speed, depending on the material and surface of the wall.

## 2. What is the coefficient of restitution and how does it relate to ball rebounding off a wall?

The coefficient of restitution is a measure of the elasticity of a ball. It is defined as the ratio of the final velocity of the ball after impact to the initial velocity. The higher the coefficient of restitution, the more elastic the ball is, and it will rebound with more speed and energy off a wall.

## 3. How does the surface material of the wall affect the rebound of a ball?

The surface material of the wall can greatly impact the rebound of a ball. A harder and smoother surface, such as concrete, will result in a higher rebound, while a softer and rougher surface, such as wood, will result in a lower rebound. This is because harder surfaces provide less resistance and allow the ball to rebound with more energy.

## 4. Does the temperature of the ball or wall affect the rebound?

Yes, the temperature of the ball and wall can affect the rebound. A colder ball will be less bouncy and will result in a lower rebound, while a warmer ball will be more bouncy and will result in a higher rebound. The temperature of the wall can also impact the rebound by affecting the elasticity of the ball and the friction between the ball and the wall.

## 5. How does air pressure inside the ball affect its rebound off a wall?

The air pressure inside the ball can significantly impact its rebound off a wall. A ball with higher air pressure will be more bouncy and will rebound with more energy, while a ball with lower air pressure will be less bouncy and will result in a lower rebound. This is because air pressure affects the elasticity of the ball, with higher pressure resulting in a more elastic ball.

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