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# Ball hits rod angular momentum example

David explains how a mass can have angular momentum even if it is traveling along a straight line. Then David shows how to solve the conservation of angular momentum problem where a ball hits a rod which can rotate. Created by David SantoPietro.

## Want to join the conversation?

• I still don't quite get how the ball has angular momentum. What I see happening is a ball with regular momentum hitting a rod and causing said rod to move with angular momentum around it's axis. I mean, if the rod wasn't connected to an axis it would just rotate about it's own center of mass, so if it got hit in the middle it should move in the same direction as the ball. Just consider the point of mass where the rod was hit. If that point mass were not part of the rod and therefore not connected to the axis, it would move in the same direction as the ball, with no angular momentum. Isn't David actually describing the transfer and conversion of regular momentum in the ball to angular momentum in the rod?
I'm sure it's me and I'm just missing something, so any clarification would be appreciated. :) Thanks
• I know this is an old comment but I think this may help future viewers. You have the right idea, but you have to be careful when you say "transfer and conversion of regular momentum in the ball to angular momentum in the rod." They are completely different quantities with different units. As you said, if the ball hit the pivot, then no angular momentum would be created. Therefore we know the angular momentum does not depend solely on linear momentum, but on linear momentum and some other quantity, in this case, the radius of closest approach. Therefore we can say relative to some origin (in this case the pivot), the ball has some angular momentum that is equal to the linear momentum times that radius. It is sort of artificial and can be confusing, but necessary in order to solve the problem. Think of it like a torque on a rod, the amount of torque depends on both the perpendicular force and the distance along the rod at which that force acts, not JUST the force, the same basic principle holds true for angular momentum.
• can we solve this problem by energy conservation
• But there is conservation of energy.

Where does the kinetic energy go if it is not all converted from the ball to the rod?
• Can anyone tell me why is the moment of inertia for the rod 1/3 MLsquared? I do not quite understand. Thanks in advance. (At )
• I don't understand why we have to take the sin of theta. Could someone please explain? Thanks
• Because angular momentum is
L = m (r x v)
The (r x v) is the cross product between the radius and velocity vectors, which when you take the magnitude it reduces to
|L| = m * |r| * |v| * sin(Θ)
• How did the torque become zero?
• When did the torque become zero? I can help you out if you can tell me when this happened in the video.
• If the ball hits the rod at the axis, the rod wouldn't rotate. Now, where does the angular momentum of the ball go. Because according to the law of conservation of angular momentum, it should be going somewhere. NO?
• no, because if the ball is moving straight towards the axis, it has no angular momentum relative to that axis. See my comment to the top question. Think of it as a set of polar coordinates, if the ball is moving towards the axis then the angle is the same for each step of the ball's motion. Try drawing the axis as a dot ad the ball as a dot, and draw a line between the two at each step of its motion. you will see the ball is going towards the axis, every point will be on a straight line. Otherwise each time it will be at a different angle.
• What if the ball after hitting the rod did not stop and went on straight with a speed of +2m/s. Is this situation the same as described at ?
• Yes. You are going to add another momentum with +2 velocity becouse the +6 velocity is transfered to rod and +2 is stayed within the ball as momentum is always conserved .
• why is the moment of inertia for the rod 1/3 MLsquared? Isnt it supposed to be 1/12 MLsquared?
• That is if the point of rotation is in the center of the rod
• But what happens to total momentum ?
Is it linear + angular momentum ??
• They are 2 entirely different concepts. You can not add apples with oranges . Linear momentum is measure of motion ( momentum) contained in the body , it does not depend upon what origin you are choosing . But angular momentum is always about some Origin , and its value keeps on changing depending upon the origin about which it is being calculated.
• So i did the problem if the ball bounces back with 2m/s, and i got the final angular velocity to be 3.75rad/s, which is greater than when ball stops. How is that make sense? When the ball stops all the momentum got transferred to the rod, but when ball bounces back, only part of it go transferred, shouldnt the final angular velocity of the rod be less?