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Angular Kinematics Chapter 6 KINE 3301 Biomechanics of Human Movement

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Radian A radian is a ratio variable. The arc length (s) is divided by the radius (r).

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Segment Angles & Joint Angles A segment angle is the angle from the right horizontal to the segment. A joint angle is the angle between two segments.

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Angular Variables & Right Hand Rule Right Hand Rule: Curl the fingers of your right hand in the direction of rotation and your thumb points in the direction of the angular motion vector.

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Angular Velocity Angular velocity is the rate of change of the angular position, or the slope of the angle – time curve. The units for angular velocity are r/s. The direction of the angular velocity vector is defined by the right hand rule.

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Angular Acceleration Angular acceleration is the rate of change in angular velocity. The units for angular acceleration are r/s 2. The direction of the angular acceleration vector is defined by the right hand rule.

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The relationship between linear and angular velocity is defined by the equation below. The angular velocity must be in r/s.

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Tangential & Radial Acceleration An object rotating has two linear accelerations. Tangential acceleration is tangent to the path and centripetal acceleration is directed toward the center of rotation. The units for a c and a T are m/s 2.

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Tangential Acceleration The tangential acceleration represents the acceleration necessary to change the rate of rotation. It is tangent to the path with units of m/s 2. If the object is rotating at a constant velocity tangential acceleration is zero.

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Centripetal Acceleration Centripetal acceleration is directed inward towards the center of the circle. To keep an object rotating in a circle it must be accelerated with a centripetal acceleration. The units for centripetal acceleration are m/s 2.

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Centripetal Force If you multiply the centripetal acceleration by mass you get the centripetal force. The centripetal force is the force necessary to keep an object rotating in a circle, it has units of N and like centripetal acceleration it is directed inward toward the center of the circle.

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A track athlete increases her velocity from V i = 7.8 m/s to V f = 8.4 m/s in a time of 0.8 s, what was the tangential acceleration ( a T )? Compute centripetal force (Fc) necessary to swing a 7.6 kg bowling ball with a velocity of 12 m/s and a radius of 1.2 m.

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