Angular Momentum The “inertia of rotation” of rotating objects is called angular momentum (L). This is analogous to “inertia of motion”, which was momentum.

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Presentation transcript:

Angular Momentum The “inertia of rotation” of rotating objects is called angular momentum (L). This is analogous to “inertia of motion”, which was momentum. (Linear momentum  mass  velocity) Angular momentum (L)  rotational inertia (I) angular velocity (ω) or L = I ω Also used … Angular momentum (L)  mass (m) x tangential velocity (v)  radius (r) or L=mvtr

Rotational version of Newton’s first law: An object or system of objects will maintain its angular momentum unless acted upon by an external net torque. (or … An external net torque is required to change the angular momentum of an object.)

Conservation of Angular Momentum The law of conservation of angular momentum states: If no external net torque acts on a rotating system, the angular momentum of that system remains constant. *Analogous to the law of conservation of linear momentum: If no external force acts on a system, the total linear momentum of that system remains constant.

Angular Momentum CHECK YOUR NEIGHBOR Suppose you are swirling a can around and suddenly decide to pull the rope in halfway; by what factor would the speed of the can change? L=Iω or L=mVr ?? Double Four times Half One-quarter 4

 mass x tangential speed  radius Angular Momentum CHECK YOUR ANSWER Suppose you are swirling a can around and suddenly decide to pull the rope in halfway, by what factor would the speed of the can change? Double Four times Half One-quarter Explanation: Angular Momentum is proportional to radius of the turn. No external torque acts with inward pull, so angular momentum is conserved. Half radius means speed doubles. Angular momentum  mass x tangential speed  radius 5

Conservation of Angular Momentum Demo…Person with bricks on spinning disk Demo…Batter on spinning disk Initial angular momentum (L) =0…..final L=0

Angular Momentum CHECK YOUR NEIGHBOR Suppose by pulling the weights inward, the rotational inertia of the man reduces to half its value. By what factor would his angular velocity change? Double Three times Half One-quarter A. double 7

 rotational inertia  angular velocity Angular Momentum CHECK YOUR ANSWER Suppose by pulling the weights in, if the rotational inertia of the man decreases to half of his initial rotational inertia, by what factor would his angular velocity change? Double Three times Half One-quarter Explanation: Angular momentum is proportional to “rotational inertia”. If you halve the rotational inertia, to keep the angular momentum constant, the angular velocity would double. Angular momentum  rotational inertia  angular velocity 8

HW #8-3 Handout