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Review Sheet _7

Review Sheet _7 - axis but displaced from it by a distance...

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Rev. 1 REVIEW SHEET #7: Dynamics of Rotational Motion: Torque, Newton’s 2nd Law, Moment of Inertia, Work, Kinetic Energy, Angular Momentum, Conservation of Angular Momentum The angular acceleration of a rigid body is caused by a net torque acting on it: Torque (a vector) is defined as r F τ = × r r r ; its magnitude is sin r F θ = r r r ( F r is a force applied to a rigid body at a point P and r r is the position vector that locates point P relative to the axis of rotation) Newton’s Second Law for Rotation : ext I α = ⋅ r r ( I = Moment of Inertia) Definition of Moment of Inertia: 2 i i i m r I = (a scalar quantity) (m i = the mass elements that make up a rotating rigid body and r i = the radius at which the center of mass of mass element m i rotates about the axis) Parallel Axis Theorem : If the moment of inertia of a rigid body of mass M rotating about an axis that passes through the body’s center of mass is CM I , then the moment of inertia of the same body rotating about any other axis that is parallel to the original
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Unformatted text preview: axis but displaced from it by a distance d is given by 2 P CM Md I I + = Definition of Work done by a constant torque : 2 1 ( ) z z W = ⋅-= ⋅∆ A rotating rigid body has Kinetic Energy : 2 1 2 K I ϖ = The Angular Momentum (a vector) of a point mass m is defined as L r p r mv = × = × r r r r r ( p mv = r r is the linear momentum of m and r r is the position vector that locates the point mass relative to the axis of rotation) The magnitude is sin L r p = ⋅ ⋅ r r r ; the direction is determined by the right-hand rule. For a rigid body rotating about a symmetry axis, L I = r r Conservation of Angular Momentum : for any system of particles ext dL dt = ∑ r r From this it follows that constant L = r if ext = ∑ r . When the net external torque acting on a system is zero, the total angular momentum of the system is conserved (remains constant). Phys 0174 – Fall 2008 – P. Koehler...
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