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Linear and Angular Concepts Applied to Biomechanics Linear Angular 1. Time (t) 1. Time (t) 2. Position 2. Orientation 3. Linear displacement (d) 3. Angular displacement () 4. Linear velocity (V)= d/t 4. Angular velocity ()=/t 5. Linear acceleration (A)= V/t 5. Angular acceleration ()=/t 6. Force = mass x acceleration 6. Torque ()= force x perpendicular distance An imbalancing force causes linear An imbalancing torque causes acceleration. rotational acceleration. 7. Newton’s 1st Law - the law of 7. Newton’s 1st Law - the law of inertia inertia A body at rest remains at rest and a A body at rest remains at rest and a body in motion remains in motion in a body that is rotating remains rotating straight line unless acted upon by an unless acted upon by an outside torque. outside force. Inertia is the property of a body that resists changes in position or linear motion. Moment of inertia (I) is the property of a body that resists changes in position or angular motion. Mass (M) is a measure of inertia. I=Mr2 Note that I is a product of the mass of the rotating object and square of the distance that the mass is located from the point of rotation. 8. Newton’s 2nd Law - law of angular acceleration (also known as the Law of Angular Momentum) 8. Newton’s 2nd Law - the law of linear acceleration (also known as the Law of Momentum) The linear acceleration of an object is The angular acceleration of an object directly proportional to the force and directly proportional to the torque and inversely proportional to mass. inversely proportional to the moment of inertia. F = M x A, where F is force, M is mass and A is acceleration. Note that F = M x V/t and Ft =MxV Ft is a quantity called impulse and MV is momentum. In other words, the application of force to an object for a period of time causes the object to change its linear momentum. = I x , where I is the moment of inertia and is the angular acceleration. Note that T = I x /t and Tt = I I is a quantity called angular momentum. In other words, the application of a torque to an object for a period of time causes the object to change its angular momentum. 9. Conservation of linear momentum In any system the linear momentum does not change unless an outside force is applied to the system. 9. Conservation of angular momentum In any system the angular momentum does not change unless an outside torque is applied to the system. 10. Conservation of energy The energy of a system is conserved. Application of the conservation of angular momentum to the kinetic link principle 10. Conservation of energy The energy of a system is conserved. Potential energy (PE) = Mgh, it is energy do to position. Kinetic energy (KE) = 1/2MV2,, it is energy do to linear velocity (motion). 11. Newton’s 3rd Law - the law of action and reaction For every action (force) there is an equal and opposite reaction (force). Angular kinetic energy = 1/2xI2, it is energy do to angular velocity (motion). 11. Newton’s 3rd Law For every torque there is an equal and opposite torque. Dr. Eugene W. Brown Department of Kinesiology Michigan State University Linang.doc