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phy2048-ch11

# phy2048-ch11 - Chapter 11 Torque and Angular Momentum I...

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1 Chapter 11 – Torque and Angular Momentum I. Torque II. Angular momentum - Definition III. Newton’s second law in angular form IV. Angular momentum - System of particles - Rigid body - Conservation - Vector quantity. F r arrowrightnosp arrowrightnosp arrowrightnosp × = τ Direction: right hand rule. Magnitude: F r F r F r F r = = = = ) sin ( sin ϕ ϕ τ Torque is calculated with respect to (about) a point. Changing the point can change the torque’s magnitude and direction. I. Torque

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2 II. Angular momentum - Vector quantity. ) ( v r m p r l arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp × = × = Direction: right hand rule. Magnitude: v m r p r p r p r v m r v m r p r l = = = = = = = ) sin ( sin sin ϕ ϕ ϕ l positive barb2right counterclockwise l negative barb2right clockwise Direction of l is always perpendicular to plane formed by r and p. Units: kg m 2 /s III. Newton’s second law in angular form dt p d F net = arrowrightnosp Linear Angular dt l d net arrowrightnosp harpoonrightnosp = τ Single particle The vector sum of all torques acting on a particle is equal to the time rate of change of the angular momentum of that particle. Proof: ( ) ( ) net net F r F r a m r dt l d a r m v v a r m v dt r d dt v d r m dt l d v r m l τ arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp = × = × = × = = × = × + × =
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phy2048-ch11 - Chapter 11 Torque and Angular Momentum I...

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