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10-11-RotationalKinematics

# 10-11-RotationalKinematics - Chapter 10 Rotational...

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1 Chapter 10 Rotational Kinematics Angular Position The angle between a radial line and the chosen reference line. Analogy between Rotational kinematics and 1D kinematics: 1D kinematics Rotational Kinematics Origin of x axis Reference line Initial position x 0 Initial angular position θ 0 Position x Angular position θ Convention: Positive angle = counterclockwise When a rigid body rotates about a fixed axis, the angular displacement is the angle  swept out by a radial line Angular Displacement 1D kinematics Rotational Kinematics Δθ another radial line Displacement , Angular displacement When a rigid body rotates about a fixed axis, in a given time interval, any radial line sweeps through the same angular displacement. Just like when a rigid body moves (translates), any point on it goes through the same displacement.

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2 Angles in radians (in radians) = Arc Length Radius s r Relation between radians and degrees 2 π rad = 360 o 1 rad = 360 o /2 π 57.3 o 1 full turn: s = 2 π r θ rad =2 π r/r = 2 π 1 full turn: θ deg = 360 o Average Angular Velocity Average angular velocity Angular displacement Elapsed time t Angular velocity is the rate of change of the angle with time Unit: rad/s T 2 period s rad rad rev rpm / 30 sec 60 2 min 1 1 (1 full turn) 1D kinematics Rotational Kinematics Average velocity Average angular velocity t
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