Periods 1-2, 6-7, 8-9:
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The last type of collision involving angular momentum is the type where BOTH linear and angular momentum are conserved. This would be something like hitting a stick that lies on a tabletop. If there was no friction, then there would be no net force adn no net torque on the stick once it is moving, and therefore BOTH types of momentum would be conserved. The stick would rotate about the center of mass, and the center of mass is the one point of the stick that would move linearly. Check out the video on this type of collision and motion.
If anyone needs to review other examples of collisions and angular momentum: There are a number of instances where collisions occur with objects that rotate. Putting a golf ball is basically a rotating stick colliding with the ball. A person stepping off a playground merry go round disk, or running and then jumping on a disk, is like an 'explosion' or inelastic collision, respectively.
Or throwing gum or a dart at a ball or tire will cause rotations after they stick together. And many more (often goofy!) examples can be dreamed up.
These tend to look like (mv_i)rsin(beta 1) + (I_i)(w_i) = (mv_f)rsin(beta 2) + (I_i)(w_i). Note that if things stick together, we will need to add moments of inertia together.
Video similar to putting a golf ball
Video examples of collisions with angular momentum
HW due Friday: AP Probs (1981, 1998) on pages 4 and 9. *Work together and use SP solutions if necessary to check yourselves. Also talk through any other HW problems in your groups that you have questions on.
We are working our way through EM induction and Faraday's law, and presently the focus is on the type where induced voltage = emf = -A dB/dt. The main concept we want to understand here is that the physical reason why a current turns on is not because of magnetic forces, but instead because when a B-field changes, an electric field turns on...and this E-field circulates! This is very different from a radial E-field that we are used to in electrostatics. The circulating E-field circulates in our loops of wire, and it is the electric force, F = qE, that pushes charges in the wire loops! Weird!
So EM induction basically says:
If there is a dE/dt, a circulating B-field turns on, AND if there is a dB/dt, a circulating E-field turns on.
Check out and take notes on two videos for this type of process, with circulating E-fields. We know how to handle this because we have done Ampere's law for circulating B-fields already - it is a path integral. The first video is a stranger example of flux and how to find it, along with dB/dt, and the second video is about finding the circulating E-field that turns on in these cases.
There will be a new post for Thursday, since Doc V and a couple seniors will be in Champaign for WYSE state finals.
HW due Friday: AP Probs (2010, 1978) on pages 4 and 5. *There are worked examples in the packet, as well. Feel free to work together and check solutions online for any of this.