PHY 107 1st Edition Lecture 21 Outline of Last Lecture I. Collision and Impulse Outline of Current LectureII. RotationCurrent LectureRotation - rotational motion of rigid bodies about a fixed axis- Rigid body – one that can rotate with all its parts locked together without changing its shape- Fixed axis – one that does not move Translational Motion ↔ Rotational Motionx ↔ θv ↔ ωa ↔ αv = v0 + at ↔ ω = ω0 + αtx = x0 + v0t + at22 ↔ θ = θ 0 + ω 0t + α t22v2 - v02 = 2a(x – x0) ↔ ω2 - ω02 = 2α(θ – θ0)K = mv22 ↔ K = I ω22m ↔ IF = ma ↔ τ = IαThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.F ↔ τ P = Fv ↔ P = τω- Angular displacement: ∆θ = θ2 – θ1 All points of the rigid body have the same displacement because they rotate locked together- Angular velocity: ω (rad/sec) Average: ωavg = θ2−θ1t2−t1 = ∆ θ∆ t Instantaneous: ω = d θd t- Algebraic sign of angular frequency: Body rotates counterclockwise, ω is positive Body rotates clockwise, ω is negative- Angular acceleration: α Average: αavg = ω2−ω1t2−t1 = ∆ ω∆ t Instantaneous: α = d ωd t- Angular velocity vector Direction of ´ω is along the rotational axis Sense of ´ω is defined by the right hand ruleo Curl right hand so that the fingers point in the direction of the rotation, then the thumb gives the sense. - When α is constant: Translational Motion ↔ Rotational Motionx ↔ θv ↔ ωa ↔ αv = v0 + at ↔ ω = ω0 + αtx = x0 + v0t + at22 ↔ θ = θ 0 + ω 0t + α t22v2 - v02 = 2a(x – x0) ↔ ω2 - ω02 = 2α(θ – θ0)- Relating linear and angular velocities: Arc length s and the angle θ are connected by s = rθ v = rω T = 2 πω T = 1f ω = 2πf- Angular acceleration: Acceleration of a point P is a vector with 2 components:1. Radial (centripetal) – along radius pointing toward O αr = v2r = ω2r2. Tangential – along tangent to circular pathαt = rα α = √ar2+at2- Kinetic energy of rotation: Rotational inertia (moment of inertia):o I = ∑imiri2o I = ∫r2dmo K = ½ Iω2 - Parallel axis theorem – the rotational inertia I about an axis parallel to the axis through Othat passes through point P, a distance H from O, is given by: I = Icom + Mh2- Torque (τ) – force ´F applied at point P a distance r from O has 2
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