# Ball hitting baseball bat (with no impulse)

• SnappySeudonym
The third equation is the combination of the first two.In summary, the conversation discusses the setup for a problem involving a ball and a bat moving at different initial velocities, and the goal is to determine the distance x at which there is no impulse reaction at point A. The conversation also mentions the use of conservation of linear and angular momentum, and the potential mistake of using the center of gravity instead of the end of the rod when calculating the moment.
SnappySeudonym

## Homework Statement

Given the setup above, what distance x should the ball be away so that there is no impulse reaction at A?

## Homework Equations

Conservation of Linear and Angular momentum.

## The Attempt at a Solution

Conservation of linear momentum (←+)
(considering the bat alone)
M(vg1) + ∑ Fxdt = M(vg2)
M(vg2 - (vg1)) = ∑ Fxdt
(3/2)LM(ω2 - ω1) = ∑ Fxdt ⇒ (1)

Conservation of angular momentum (+⊃)
Igω1 + ∑ Madt = Igω2 +mux
Ig = (1/12)M(3L)2
Ig = (3/4)L2M
(3/4)L21 + ∑ (Fxdt)x = (3/4)L22 + mux
using (1)
(3/4)L21 +((3/2)LM(ω2 - ω1))x = (3/4)L22 + mux
x((3/2)LM(ω2 - ω1 - mux) = (3/4)L2M(ω2 - ω1)
x = L/(2(1-mu)

I've seen this problem before, but not with the bat/rod moving at an initial angular speed, can anyone give some insight as to where my solution is wrong, Is it because a used inertia for the COG of the bar and not the end?

#### Attachments

• FIG.JPG
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SnappySeudonym said:
Conservation of angular momentum (+⊃)
Ig = (1/12)M(3L)2
:
∑ (Fxdt)x
The first equation above appears to be taking moments about the centre of the rod (1/12), but the second expression is a moment about the suspension point (x).

## 1. How does the ball move after hitting the baseball bat without impulse?

The ball will continue to move in the same direction as it was before hitting the bat, but with a lower velocity. This is due to the conservation of momentum, where the initial momentum of the ball is equal to the final momentum of the ball and bat system.

## 2. Is there any force acting on the ball when it hits the bat with no impulse?

Yes, there is still a force acting on the ball when it hits the bat without any impulse. This force is called the normal force and it is exerted by the bat onto the ball in the opposite direction of the ball's motion.

## 3. Can the ball still travel far after hitting the bat without impulse?

No, the ball will not travel as far as it would if it had hit the bat with an impulse. This is because an impulse increases the momentum of an object, allowing it to travel further.

## 4. Does the weight of the bat affect the ball's movement after hitting it without impulse?

Yes, the weight of the bat does have an impact on the ball's movement after hitting it without impulse. A heavier bat will exert a greater force on the ball, causing it to have a lower velocity and travel a shorter distance.

## 5. How is the kinetic energy of the ball affected by hitting the bat without impulse?

The kinetic energy of the ball will decrease after hitting the bat without an impulse. This is because kinetic energy is directly proportional to the square of an object's velocity, so when the velocity decreases, the kinetic energy will also decrease.

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