Describing Rotational Motion Chapter 8

Linear to Rotational (Angular) Angular displacement: distance traveled around a circle or arc (measured in radians or rad) Angular velocity: change in angular displacement over time (measured in rad/s) Angular acceleration: change in angular velocity over time (measured in rad/s2)

Linear to Angular (Rotational) We can use the same basic principles as before. The only difference will be the motion will be in a circle rather than a straight line.

Torque A force that causes an object to rotate Measures how effective a force is in rotating an object Measured in Newton meters, Nm (in America, known at foot pounds, ft lb)

Time for Rotation Answer the following: Materials Calculator Objective Determine the angular displacement and velocity of the hands on a clock. Answer the following: How far does the second hand move every 10 s? What is the angular velocity for each hand (second, minute, hour) in rad/s? Find angular displacement in rad for each hand in 20 min? There is a speck of dust on the second hand. Where on the hand would it move the fastest? The slowest?

t = F r sin q Torque (Equation #1) Also known as force at a distance from the equation: t = F r sin q t is torque (Nm) F is force (N) r is lever arm length or radius (m) q is the angle between F and r (degrees)

Torque (Equation #2) F = m a  t = I a Using the same argument as we did with angular equations of motion, we can find an angular equation for force. F  t (torque, Nm) m  I (moment of inertia, kgm2) a  a (angular acceleration, rad/s2) F = m a  t = I a

Moment of Inertia p206 Known as rotational mass Based on shape and pivot point In general, a spinning point-sized object will have a moment of inertia of m r2 Units: kg m2 p206

Torque Lab Objective: Use knowledge of torque to balance. Materials: Meter stick Binder clips Masses Hangers Ring stand (clamp) Procedures: Set-up equipment like demo Determine the mass of the hanger holder using materials given (___ g) Place hanger with 20 g at 70 cm Calculate and record where 50 g (silver hanger) should be place on the other side for balance (_____ cm) Place silver hanger at calculated position Determine how close your results were (off by ___ cm)

Ch8 Homework 72. 0.6 rad 75. 197 rad/s, 492 rad 82. 3.8 Nm 87. 63 N right, 37 N left 91. 21 rad/s, 16 rev,100 rad