rotkin - In this case, every particle of the body is...

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Rotational kinematics Rotational kinematics involves six definitions, here we go again. time, t ● time interval, t t f - t i angular position, θ angular displacement, ∆θ≡θ f - i angular velocity, ϖ≡ d /dt angular acceleration, α≡ d ϖ /dt Note: in going from linear to angular, often we add the adjective angular . We will measure angles in radians. Recall an angle θ is given by the arc length it subtends divided by the radius of the circle, θ ≡ s/r. This definition leads to the following table: θ (in degrees) s θ (in radians) 360 2 π r 2 π 180 π r π 90 ½ π r ½ π 6 0 1/3 π r 1/3 π 4 5 1/4 π r ¼ π 3 0 1/6 π r 1/6 π
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Definition: Rigid Body A set of particles for which r ij = c ij = constant, for every pair of particles in the body, where r ij is the distance between any two particles, i and j of the rigid body. In our work we will concentrate on the rotation of a rigid body about a fixed axis of rotation.
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Unformatted text preview: In this case, every particle of the body is executing circular motion with its own radius r i . The following hold for the i th particle of the rigid body, s i = r i v i = r i (velocity) a t = r i = dv i /dt (tangential acceleration) a c = v i 2 /r i = r i 2 (radial or centripetal acceleration). CAUTION: r i is NOT the magnitude of the position vector of the i th particle, but is the radius of its circular motion. See Figure The motivation for this chapter is based on the fact that certain quantities ( and ) describe the body as a whole and not just the individual particles of the body. Special Case of Motion: Constant (t) = o + o t + t 2 and (t) = o + t . Can you guess the rotational shortcut equation? EXAMPLES(in class)...
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This note was uploaded on 07/29/2011 for the course PHY 2048 taught by Professor Chen during the Spring '08 term at UNF.

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rotkin - In this case, every particle of the body is...

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