Review Sheet _6

Review Sheet _6 - ω = ω αt Equ(2 θ θ 0 = ω t ½αt 2...

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Rev. 1 REVIEW SHEET #6: Kinematics of Rotational Motion of Rigid Bodies Definitions of kinematic quantities for rotational motion: Angular coordinate relative to a reference direction (usually +x-axis) θ [radians] Angular Displacement (vector) 2 1 θ ∆ = - [radians] Angular Velocity (vector) 2 1 2 1 ave t t t ϖ - = = - [radians/sec] inst d dt = [radians/sec] Angular Acceleration (vector) 2 1 2 1 ave t t t α - = = - [radians/s 2 ] inst d dt = [radians/s 2 ] When a rigid body rotates about a fixed axis, the directions of these vectors can be determined by using the right-hand rule. When a rigid body rotates about a fixed axis, at any instant every part of the body has the same angular velocity and the same angular acceleration. Equations of Rotational Motion with Constant Angular Acceleration: Equ. (1):
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Unformatted text preview: ω = ω + αt Equ. (2): θ - θ 0 = ω t + ½αt 2 Equ. (3): ω 2 = ω 2 + 2α(θ – θ ) Equ. (4): θ - θ = ½(ω + ω)t θ , ω , and α are constants. Note that Equ. (1) is the time derivative of Equ. (2). Relationships Between Linear and Angular Kinematic Variables: Angle θ [in radians] is defined as the ratio of the arc length s to the radius r (see Fig.9.2) s r = hence tan ds d r dt dt v r = = = and tan tan dv d r dt dt a r = = = Using tan r v = , the expression for the centripetal (radial) acceleration given on Review Sheet #3 can be written as 2 2 tan c rad v a r r a = = = Phys 0174 – Fall 2008 – P. Koehler...
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