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Rotation, angular motion & angular momentom. Physics 100 Chapt 6. Rotation. Rotation. d 2. d 1. The ants moved different distances: d 1 is less than d 2. Rotation. q. q 2. q 1. Both ants moved the Same angle: q 1 = q 2 (= q ). Angle is a simpler quantity than distance

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## Rotation, angular motion & angular momentom

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**Rotation, angular motion & angular momentom**Physics 100 Chapt 6**Rotation**d2 d1 The ants moved different distances: d1 is less thand2**Rotation**q q2 q1 Both ants moved the Same angle: q1 =q2 (=q) Angle is a simpler quantity than distance for describing rotational motion**Angular vs “linear” quantities**Linear quantity symb. Angular quantity symb. distance d angle q velocity v angular vel. w change in d elapsed time = change in q elapsed time =**Angular vs “linear” quantities**Linear quantity symb. Angular quantity symb. distance d angle q velocity v angular vel. w acceleration a angular accel. a change in w elapsed time change in v elapsed time = =**Angular vs “linear” quantities**Linear quantity symb. Angular quantity symb. distance d angle q velocity v angular vel. w acceleration a angular accel. a mass m Moment of Inertia I (= mr2) resistance to change in the state of (linear) motion resistance to change in the state of angular motion moment arm M Moment of inertia = mass x (moment-arm)2 x**Moment of inertial**M M x I Mr2 r r r = dist from axis of rotation I=small I=large (same M) easy to turn harder to turn**Angular vs “linear” quantities**Linear quantity symb. Angular quantity symb. distance d angle q velocity v angular vel. w acceleration a angular accel. a mass m moment of inertia I Force F (=ma) torque t (=I a) Same force; bigger torque Same force; even bigger torque torque = force x moment-arm**Teeter-Totter**His weight produces a larger torque F Forces are the same.. but Boy’s moment-arm is larger.. F**Angular vs “linear” quantities**Linear quantity symb. Angular quantity symb. distance d angle q velocity v angular vel. w acceleration a angular accel. a mass m moment of inertia I torque t (=I a) Force F (=ma) angular mom. L(=I w) momentum p (=mv) Iw = Iw Angular momentum is conserved: L=const**Conservation of angular momentum**Iw Iw Iw**High Diver**Iw Iw Iw**Angular momentum is a vector**Right-hand rule**Conservation of angular momentum**Girl spins: net vertical component of L still = 0 L has no vertical component No torques possible Around vertical axis vertical component of L= const**Turning bicycle**These compensate L L**Torque is also a vector**example: pivot point another right-hand rule F t is out of the screen Thumb in t direction wrist by pivot point F Fingers in F direction**Spinning wheel**t wheel precesses away from viewer F**Angular vs “linear” quantities**Linear quantity symb. Angular quantity symb. distance d angle q velocity v angular vel. w acceleration a angular accel. a mass m moment of inertia I torque t (=I a) Force F (=ma) momentum p (=mv) angular mom. L(=I w) kinetic energy ½mv2 rotational k.e. ½I w2 w I V KEtot = ½mV2 + ½Iw2**Hoop disk sphere race**I I I**Hoop disk sphere race**I KE = ½mv2 + ½Iw2 KE = ½mv2 + ½Iw2 I KE = ½mv2 + ½Iw2 I**Hoop disk sphere race**Every sphere beats every disk & every disk beats every hoop

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