Rotational Motion NCEA AS 3.4 Text Chapter: 4

Types Pure Translation –force acts through the centre of mass, C.o.m moves. Pure Rotation –2 equal & opposite forces act at a perpendicular distance from the c.o.m (force couple) C.o.m remains stationary, object spins around it Mixture – single force acts, NOT through c.o.m, object moves and rotates around c.o.m

Angular Displacement Although both points A & B have turned through the same angle, A has travelled a greater distance than B A must have had the greater linear speed B A q

Angular Displacement Symbol q Measured in radians (rad) s Angular displacement is related to linear distance by: q r s

Angular Displacement Remember from Maths: r How to put your calculator into radian mode? How many radians are in a full circle? r

Angular Velocity Symbol w Measured in radians per second (rads-1.) Average angular velocity calculated by:

Angular Velocity s r q To put it another way: So angular velocity is related to linear velocity by:

Angular Acceleration Changing angular velocity Symbol: a Measured in radians per second squared (rads-2.) Calculated by:

Angular Acceleration Angular acceleration and linear acceleration are linked by:

Summary Translational Rotational Equation s q s=rq v w v=rw a a=ra

Gradient = angular velocity w Graphs

Graphs Area under graph = angular displacement q Gradient = angular acceleration a

Kinematic Equations Recognise these??: Use them the same way you did last year.

Torque F Torque is the turning effect of a force. Symbol: t Measured in Newton metres (Nm) Acts clockwise or anticlockwise Force and distance from pivot must be perpendicular

Torque Just as force causes linear acceleration, torque causes angular acceleration. So what is this “I” thing anyway….

Rotational Inertia Symbol: I Measured in kgm2 Rotational inertia is a measure of how hard it is to get an object spinning. It depends on: Mass How the mass is distributed about the axis of rotation

Angular Momentum Any rotating object has angular momentum, much the same as any object moving in a straight line has linear momentum. Angular momentum depends on: The angular velocity w The rotational inertia I Symbol: L Measured in kgm2s-1

Angular momentum Angular momentum is conserved as long as….. There are no external torques acting.

Angular Momentum Linear momentum can be converted to angular momentum

Rotational Kinetic Energy The energy of rotating objects Ek(rot)

Rolling Down Slopes Which will reach the bottom first?