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10 Rotational Motion ay

# 10 Rotational Motion ay - Chapter 10 Rotational Motion...

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1 Chapter 10 Rotational Motion About a Fixed Axis

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3 10-1 Angular Quantities l = R θ Circle = 360 o = 2 π rad = 1 rev l = R θ

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4 Tangential velocity v = Δ l Δ t ,______ ω = Δ θ Δ t ,_____ Δ l = R Δ θ v = ω R a tan = dv dt = R d ω dt = R α _______ α = d ω dt a rad = v 2 R
5 Frequency Relating angular velocity to the frequency, f , ( ν ) of rotation, where frequency means the number of revolutions per second. One revolution corresponds to 2 π radians. 1 rev/s = 2 π rad/s. 1 Hz (Hertz) = 1 rev/s. ω 2 π f = ; ω = 2 π f

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6 The Vector Nature of Angular Quantities ω and α are referred to a “ pseudo” vectors . The only unique direction associated with rotation is along the axis of rotation. Which way is UP ? Use the “right hand rule.”
7 10-3 Kinematic Equations for Uniformly Accelerated Rotational Motion Angular θ = ω ο t + ½ α t 2 ω = ω ο + α t ω 2 = ω ο 2 + 2 αθ Linear x = v o t + ½ at 2 v = v o + at v 2 = v o 2 + 2 ax These equations are valid only for constant a and α .

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8 10-4 Torque Torque ( τ ) deals with the dynamics of rotational motion. In rotational motion TORQUE is analogous to FORCE in linear motion. That is, force through a distance F τ
9 Torque τ = RF = RF sin θ * Torque is a vector (TBD in Chapter 11). τ = R x F = RF sin θ These two methods of calculation are completely equivalent.

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11 Torque on a compound wheel.

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