# g8 - Kinetic Variables for Rotation • Angular position...

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Unformatted text preview: Kinetic Variables for Rotation • Angular position θ (in radians) • Angular displacement Δ θ = = θ 2 − θ 1 • Angular velocity ω = Δ θ/ Δ t (instantaneous a.v.: Δ t → ) • Angular acceleration α = Δ ω/ Δ t (instantaneous a.a.: Δ t → ) c circlecopyrt L.Frommhold . – p.27/27 Distance Travelled Along the Arc • Rotation: distance Δ ℓ travelled along the arc, Δ ℓ = r Δ θ where r is the radius of the circle; angles are expressed in rad units. • (Tangential) velocity v = Δ ℓ Δ t = r Δ θ Δ t = r ω • (Tangential) acceleration a = Δ v Δ t = r Δ ω Δ t = r α c circlecopyrt L.Frommhold . – p.26/27 Linear and Rotational Quantities c circlecopyrt L.Frommhold . – p.25/27 Radial and Tangential Acceleration • Centripetal (=center seeking) acceleration keeps particle P on circular path • Tangential accel- eration (if present) accelerates particle speed • Acceleration of P is the vector sum of radial and tangential accelerations. c circlecopyrt L.Frommhold . – p.24/27 Rotational Speed • Rotational speeds are commonly specified in units of revolutions per minute (or per second ), 1 rev / s = 2 π rad / s • Frequency of revolution f = ω 2 π • Duration of one complete revolution (“period”) T = 1 f c circlecopyrt L.Frommhold . – p.23/27 Constant Angular Acceleration • Kinematic equations for constant α ω = ω + αt v = v + at θ = ω t + 1 2 αt 2 x = v + 1 2 at 2 ω 2 = ω 2 + 2 αθ v 2 = v 2 + 2 ax ω = ω + ω 2 v = v + v 2 • Completely analogous to linear kinematic equations with constant acceleration c circlecopyrt L.Frommhold . – p.22/27 Rolling Motion v = rω c circlecopyrt L.Frommhold . – p.21/27 How Forces Produce Rotation...
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g8 - Kinetic Variables for Rotation • Angular position...

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