Lect_21 - Review of circular motion Lecture 21 Rotations of...

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Lecture 21 Rotations of a Rigid Body. Moment of inertia Review of circular motion ; ; dd dt θ ω θω α == vR = y x s R Relation to linear quantities: s = R Description in terms of angular quantities (in radians!): tan aR = Centripetal acceleration 2 2 c v a tan c total Angular velocity Example: A rod on the plane of the page rotates about an axis through one of its ends at 0.25 rpm. If the initial position is as shown, what is its position at t = 1 min? = 0 Or this? This? We need to indicate whether the motion is CW or CCW! Angular velocity : •Magn itude • Direction: perpendicular to the plane of motion and in the direction given by the RHR. dv The right-hand rule (again) • Curl fingers of right hand in the direction of motion. • Stick thumb out. This is the direction of angular velocity ω CCW from above CW from above ω
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ACT: Wall clock A. Into the wall. B. Out of the wall. C. Nothing, it’s zero. ωω GG Let and be the angular velocities of the large and the small handles of the wall clock in this room. What is the direction of the difference - ? S L Both and point into the wall. ω > G G Angular acceleration Angular acceleration α : •Magn itude • Direction: perpendicular to the plane of motion, parallel (antiparallel) to if the system is speeding up (slowing down). tan a d dt R == ω α Speeding up ω α Slowing down When the plane of rotation is constant, we can always choose that plane to be the xy plane. ω α x y z > 0; > 0 Then, all that matters is the sign of and . Speeding up ω α < 0; < 0 Speeding up ACT: Angular acceleration A ball rolls across the floor and then starts up a ramp as shown below. In what direction does the angular acceleration vector point when the ball is on the ramp? A. Down the ramp B. Into the page C. Out of the page is into the page Ball is slowing down is out of the page
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Rigid body Rigid body A rigid body is a system where internal forces hold each part in the same relative position. Motion which a rigid body: * Motion of the center of mass -in response to an external force. * Rotations about the CM. Or * Rotations about a fixed axis Energy of Rotational Motion Energy of Rotational Motion = = n i v m K 1 2 2 1 tot Consider a rigid body being rotated around an axis parpendicular to the page and through point P. The body can be broken down into n particles. 1 2 3 P 3 2 1 ω = = r 1 2 2 1 ) ( 2 1 2 2 1 = = 2 2 1 rotational I = Moment of inertia (about this axis): = = 1 2 1 3 2 Perpendicular distance between the axis and the particle = Moment of Inertia = = 1 2
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This note was uploaded on 04/16/2008 for the course PHYSICS 221 taught by Professor Johnson during the Fall '06 term at Iowa State.

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Lect_21 - Review of circular motion Lecture 21 Rotations of...

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