# UMass Amherst KIN 100 - angular-kinetics-2 (13 pages)

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- Pages:
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- School:
- University of Massachusetts Amherst
- Course:
- Kin 100 - Introduction to Kinesiology

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Newton s Laws of Motion Angular Analogues Newton s First Law A rotating body will maintain a state of constant rotational motion unless acted on by an external torque Resistance to Acceleration Resistance to linear acceleration Mass Resistance to angular acceleration Moment of Inertia Moment of inertia is determined by mass and mass distribution relative to axis of rotation Determining Moment of Inertia Determining Moment of Inertia Moment of inertia is the sum of the products of all the mass elements of an object and the square of the distances of the mass elements from the axis of rotation A more practical approach Iaxis miri2 where is an experimentally determined length known as the radius of gyration that applies to the whole object r1 m1 axis Iaxis mbody 2 m2 r2 Iaxis m1r12 m2r22 mnrn2 is not the same as the distance to segment CM magnitude of is different for different axes of rotation Unit for moment of inertia consists of unit of mass multiplied by unit of length squared kg m2 1 Human Body Moment of Inertia Can be computed for Applications Chocking up on a baseball softball bat individual body segments forearm thigh etc the whole body Tuck vs layout position of a diver or gymnast Typically expressed for an axis through the center of mass or through the proximal or distal end layout tuck Position of a runner s leg during the swing phase moment of inertia of the whole body about different axes of rotation hip 13 5 kg m2 11 5 kg m2 4 5 kg m2 1 5 kg m2 2 5 kg m2 Angular Momentum Angular Momentum Momentum A 57 g tennis ball is struck by a racket giving it an angular momentum of 6 8 10 4 kg m2 s If the radius of gyration of the ball is 2 4 cm how fast will it be spinning For linear motion For angular motion Or M mv H I topspin forehand shot H m 2 Factors that affect angular momentum mass of the object m distribution of mass relative to axis of rotation angular velocity of the object Units for angular momentum kg m2 s H I m 2 0 00068 kg m2 s 0 057 kg 0 024 m 2 0 00068 kg m2 s 0 000033 kg m2 20 6 rad s 1180 deg s 3 28 rev s 2 Conservation of Angular Momentum The total angular momentum of a given system remains constant in the absence of external torques H is constant Conservation of Angular Momentum A 60 kg diver is in a layout position with radius of gyration of 0 5 m as he leaves the board with an angular velocity of 4 rad s What is the diver s angular velocity when he assumes a tuck position reducing his radius of gyration to 0 25 m However I and can change so long as their product remains constant recall that H I Conservation of Angular Momentum First

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