Lecture_28_web_2007

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Unformatted text preview: Quiet please ladies and gentlemen The lecture is about to begin n Kinetic energy of rolling motion R Q. What happens if the mass and radius of the object are the same but the moment of inertia is different? i i f f KE PE KE PE + = + KE = f T R KE KE KE = + R υ ϖ = 2 1 2 k Mgh M υ + = ÷ 2 1 gh k υ = ÷ + i PE mgh = f PE = 0 0 f mgh KE + = + 2 2 1 2 k Mgh MR ϖ + = ÷ 2 2 1 gh k υ = ÷ + 2 2 2 2 1 1 2 2 KE MR kMR ϖ ϖ = + 2 regular I kMR = The smaller k is the larger v will be Lecture 27 in a nutshell • Rolling motion • The linear acceleration of an object rolling down an incline does not depend on mass for the same reason as all objects fall to the ground with the same acceleration. • If an object slips down an incline (without friction) its translational velocity will always be larger than if it is rolling, because in rolling motion kinetic energy is shared between translational and rotational motion • The smaller the 'k' value is for a rolling object, the more the kinetic energy goes in to the translational kinetic energy (hence v is higher) • Pulleys with friction and a wheel with mass • T 1 does not equal T 2 • There will be three Newtons 2nd law equations, the one for the wheel will be a rotational acceleration equation • Every part of the string has the same linear acceleration as does every part of the rim of the wheel • See online tutorial about rotation and pulleys Pulley with finite mass Two objects with masses m1=20kg and m2=15kg are connected by an inelastic string over a pulley with finite mass M as shown on the figure. The incline of the wedge is θ=37 degrees. When released, figure....
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