Lecture 22 - Lecture 22 pls-22.1 Rotational Dynamics Media...

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Lecture 22 pls-22.1 Rotational Dynamics Media: 1. Hoop and disc rolling down an incline 2. Rotating stool w/ dumb bells, bicycle wheel 1. Linear-Motion—Rotational-Motion Correspondences Concept Linear Motion Rotational Motion position x θ velocity x v ω acceleration x a α acceleration cause x F τ inertia m I N’s 2nd = i ix x F m a 1 = i i I τ α 1 K.E. 2 2 1 x v m 2 2 1 ω I work x F x θ τ power x x v F ω τ momentum x v m ω I = τ torque, = I moment of inertia 2. Moment of Inertia For a rigid body the moment of inertia I is related to the body’s resistance to changing its angular velocity. Corresponds to mass m of linear motion. Depends on mass m , shape of object, and the rotational axis .
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Lecture 22 pls-22.2 General expression: = i i i r m I 2 units = kg m 2 . Simple formulae for symmetric objects (mass M ): Ring, axis at center: 2 MR I = , = R radius of ring Solid disc, axis at center: 2 2 1 MR I = , = R radius of ring Rod, axis at center of rod: 2 12 1 ML I = = L length of rod Rod, axis at end of rod: 2 3 1 ML I = = L length of rod 3. N’s 2nd Law The rotational form of N’s 2nd Law for a rigid body is = i i I τ α
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