p111_lecture15

# p111_lecture15 - 7.5 Center of Mass The center of mass is a...

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7.5 Center of Mass The center of mass is a point that represents the average location for the total mass of a system. 2 1 2 2 1 1 m m x m x m x cm + + =

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7.5 Center of Mass 2 1 2 2 1 1 m m x m x m x cm + ! + ! = ! 2 1 2 2 1 1 m m v m v m v cm + + = The motion of the center-of-mass is related to conservation of momentum. Consider the change in the positions of the masses in some short time Δ t : Divide by Δ t
7.5 Center of Mass 2 1 2 2 1 1 m m v m v m v cm + + = In an isolated system, the total linear momentum does not change, therefore the velocity of the center of mass does not change. } P 2 1 m m + = P

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7.2 The Principle of Conservation of Linear Momentum Example: Ice Skaters Starting from rest, two skaters push off against each other on ice where friction is negligible. One is a 54-kg woman and one is a 88-kg man. The woman moves away with a speed of +2.5 m/s. Find the recoil velocity of the man.
7.2 The Principle of Conservation of Linear Momentum o f P P r r = 0 2 2 1 1 = + f f v m v m 2 1 1 2 m v m v f f ! = ( ) ( ) s m 5 . 1 kg 88 s m 5 . 2 kg 54 2 ! = + ! = f v

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7.5 Center of Mass 0 2 1 2 2 1 1 = + + = m m v m v m v cm BEFORE AFTER 0 ! = = cm v (54 kg)(+2.5 m/s) + (88 kg)(-1.5 m/s) 54 kg + 88 kg 0.02 Consider the “Ice Skater” example which was an isolated system:
Chapter 8 Rotational Kinematics

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8.1 Rotational Motion and Angular Displacement In the simplest kind of rotation, points on a rigid object move on circular paths around an axis of rotation.
8.1 Rotational Motion and Angular Displacement The angle through which the object rotates is called the angular displacement. o ! " = #

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8.1 Rotational Motion and Angular Displacement DEFINITION OF ANGULAR DISPLACEMENT When a rigid body rotates about a fixed axis, the angular displacement is the angle swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly. By convention, the angular displacement is positive if it is counterclockwise and negative if it is clockwise.
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## This note was uploaded on 06/03/2011 for the course PHY 111 taught by Professor Bolland during the Fall '10 term at Ohio State.

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p111_lecture15 - 7.5 Center of Mass The center of mass is a...

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