Angular Momentum 1)What determines how fast an object rotates? 2)Is Angular Momentum conserved?

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Presentation transcript:

Angular Momentum 1)What determines how fast an object rotates? 2)Is Angular Momentum conserved?

Day 1: Moment of Inertia  In straight line motion momentum = mass x velocity.  When objects are rotating or turning, where the mass is located is also important. See the short Demo on Moment of Inertia below to see how distribution of mass effects the momentum of an object.  (This is an easy one to do in the class or at home.)  Which stick was harder to rotate? Explain why.

Day 1: continued The stick with the masses closer to its center was easier to rotate because it has a lower moment of inertia. How the mass is distributed around on object is called its moment of inertia or rotational inertia. The farther the mass is from the center of rotation the higher the rotational inertia and the harder the object is to rotate. Just like heavier objects take more force to accelerate than lighter objects.

Day 2: Continued Another demo, but no video (sorry, no YouTube access). Two wheels have the same mass and same diameter but one is hollow. Which wheel will reach the bottom first? Explain why.

Day 2: Answer The solid disk will win because it has a smaller rotational inertia. More of its mass is located around its center of mass make it easier to rotate. This is the same reason why racing bike tires are so thin. Racers want as little as rotational inertia as possible. It has nothing to do with reducing friction.

Day 3: Conservation of Angular Momentum  How do you calculate the objects moving in a straight line? Momentum = Mass x Velocity  Rotating objects also have momentum called angular momentum. Angular Momentum = Rotational Inertia X Rotational Speed

Day 3: Law Conservation of Angular Momentum Just like linear momentum, angular momentum is always conserved in a closed system. You see examples of the of Law of Conservation of Angular Momentum everyday. Watch the video and use the Conservation of Angular Momentum to try to explain what is happening? rotation_two_balls.mpeg (Windows Media Player) rotation_two_balls.mpeg rotation_two_balls.rm (Real Player) rotation_two_balls.rm

Day 3: Answer The man is initially rotated with a certain amount of angular momentum by his assistance. When the man pulls the weights closer to his body his rotational inertia decreases so his rotational velocity must increase in order to conserve angular momentum. This is the same reason why ice skaters spin faster when they move their hands and legs closer to their body.

Day 4: Review 1.Which stick has a higher rotational inertia? Which stick will be easier to rotate. A B 2.Which roll of toilet paper would be easier to pull a sheet of paper from? (Relevancy!!!)

Day 4: Review 3. Which Diver will spin faster? Explain why using the conservation of angular momentum.

Day 4: Answers 1.Stick A has a higher rotational inertia because its mass is located farther from the center. Stick B will be easier to rotate because of a lower rotational inertia. 2.The larger toilet will be easier to pull a sheet of toilet paper from. It has a larger rotational inertia and will be harder to rotate. Therefore, there will be more tension in the toilet paper making it easier to tear. 3.If both divers leave the board with the same angular momentum, the diver in the tuck position will spin faster because they have a smaller rotational inertia and, therefore, have a higher rotational velocity to conserve angular momentum.

Day 5 Quiz (Holy Rollers!!)