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lecture9 - Phys 2101 Gabriela Gonzlez 2 3 Pure rotation of...

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Unformatted text preview: Phys 2101 Gabriela Gonzlez 2 3 Pure rotation of a reference line in a solid body around an axis is described with an angle as a function of time. =s/r ccw: positive cw: negative radians rad/sec rad/sec 2 4 2 2 1 at t v x x at v v + + = + = 2 2 1 t t t + + = + = x x 4 2 2 1 at t v x x at v v + + = + = 2 2 1 t t t + + = + = x x y 5 Trajectory is a circle (circular motion) Speed is constant (uniform motion) but velocity is not constant!? ) ( ) sin( ) cos( ) ( ) cos( ) sin( ) ( ) sin( ) cos( ) ( 2 2 2 t x j t R i t R t a j t R i t R t v j t R i t R t x = = + = + = R R v a R v R s 2 2 ; ; = = = = Derive the following formulae: 6 r s = r v r dt d dt ds = = r a r dt d dt dv t = = If speed is not constant, there is angular and tangential acceleration, apart from radial acceleration. If speed is constant, there is no angular acceleration, but there still is radial acceleration. Assume a constant radius: circular motion r a r 2 = 7 A wheel A of radius r A = 10 cm is coupled by belt B to wheel C of radius r C = 25 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s 2 . Find the time for wheel C to reach a rotational speed of 100 rev/min, assuming the belt does not slip. speed of 100 rev/min, assuming the belt does not slip....
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lecture9 - Phys 2101 Gabriela Gonzlez 2 3 Pure rotation of...

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