physics help sheet - 2 ½ mv 2 rolling without slipping = v r omega = = Torque r F sin phi torque I alpha = Torque r distance cross F

= / -> omega dtheta dt right hand rule = ; = f ma torque Ialpha = / Alpha domega dt Omega and alpha can be negative Constant acceleration = V v 0 + = at omega omega 0 + alphat = X x 0 + v 0 + t ½ at 2 = theta theta 0 + omega 0 + t ½ lphaat 2 V 2 = v 0 2 + ( - 2a x x 0 ) omega 2 = omega 0 2 + ( - 2aloha theta theta 0 ) = * = * W F s W torque delta theta = / = * = * P W t P F v P torque omega = ( ) V r omega rolling without slipping a tan = r alpha : = . .: = = Momentum p mv Ang Mom L I omega I omega I omega A rad = v 2 / r a rad = r omega 2 A total = ( root a rad 2 + a tan 2 ) -> a linear : = Moment of inertia k ½ I omega 2 = I mr 2 for ring and cylindrical shell = / I 2 5 mr 2 solid sphere = / I 2 3 mr 2 hollow sphere = Total Kinetic energy ½ I omega

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Unformatted text preview: 2 + ½ mv 2 : rolling without slipping = v r omega = = Torque r F sin phi torque I alpha = ( ) Torque r distance cross F – ( ) Initial angular momentum about disk Rmv object hitting disk Pendulum : = -( ) F mg sin theta angle between straight down and rod = ( / ) = ( / ) = ( / ) = Omega root k m root mg mL root g L omega 2pif = / ( ) 2pi T period and frequency = ( / ) . T 2 pi root L g period only depends on length and gravity = ( + ) = S A cos omega t phi A Ltheta max...
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