(21) Rotations of a Rigid Body, Moment of Intertia

# (21) Rotations of a Rigid Body, Moment of Intertia -...

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Lecture 21 Rotations of a Rigid Body. Moment of inertia

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Review of circular motion ; ; d d dt dt θ ϖ α = = v R = y x s R Relation to linear quantities: s = R Description in terms of angular quantities (in radians!): t an a R = Centripetal acceleration 2 2 c v a R R = = a tan a c a 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? t = 0 Or this? This? We need to indicate whether the motion is CW or CCW! Angular velocity ω : Magnitude Direction: perpendicular to the plane of motion and in the direction given by the RHR. d v dt R θ ϖ= =

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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
ACT: Wall clock A. Into the wall. B. Out of the wall. C. Nothing, it’s zero. ϖ r r r r Let and be t he angular velocit ies of t he lar ge and t he small handles of t he wall clock in t his r oom. What is t he dir ect ion of t he dif f er ence - ? S L S L Bot h and point int o t he wall. S L S L r r S r L r S L - r r

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Angular acceleration Angular acceleration α : Magnitude Direction: perpendicular to the plane of motion, parallel (antiparallel) to ω if the system is speeding up (slowing down). t an a d dt R ϖ α= = 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 ω z > 0; α z > 0 Then, all that matters is the sign of ω z and z . Speeding up ω α x y z ω z < 0; z < 0 Speeding up

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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 ω ω ω is into the page Ball is slowing down α is out of the page
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.

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## This note was uploaded on 03/27/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Fall '08 term at Iowa State.

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(21) Rotations of a Rigid Body, Moment of Intertia -...

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