#### Transcript Rotational Mechanics

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 A B q B A Angular Displacement q ► Measured in radians (rad) ► Angular displacement is related to linear distance by: ► Symbol s q r s r q r Angular Displacement ► Remember Maths: r s 2r from How to put your calculator into radian mode? How many radians are in a full circle? Angular Velocity w ► Measured in radians per second (rads-1.) ► Average angular velocity calculated by: ► Symbol angular displaceme nt average angular ve locity time taken w q t Angular Velocity ► To s q put it another way: q w t s s w (since q ) r t r v s w (since v ) r t r r ► So angular velocity is related to linear velocity by: v rw Angular Acceleration ► Changing angular velocity ► Symbol: a ► Measured in radians per second squared (rads-2.) ► Calculated by: change in angular ve locity angular accelerati on time taken w a t Angular Acceleration ► Angular a ra acceleration and linear acceleration are linked by: Summary Translational Rotational Equation s q s=rq v w v=rw a a a=ra Graphs Angular Displacement Angular Displacement vs Time 0 10 20 Time 30 Gradient = angular velocity w 40 Graphs Gradient = angular acceleration a Angular Velocity Angular Velocity vs Time Area under graph = angular displacemen tq 0 1 2 Time 3 4 Kinematic Equations ► Recognise these??: ► Use them the same way you did last year. w f wi a t w w 2aq 2 f 2 i q wi t 2 a t 1 2 w f wi t q 2 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 F ► Torque r t Fr Torque ► Just as force causes linear acceleration, torque causes angular acceleration. t Ia ► 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 I mr 2 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 L Iw Angular momentum ► Angular as….. ► There momentum is conserved as long are no external torques acting. Angular Momentum ► Linear momentum can be converted to angular momentum L mvr ( L pr ) r v m Rotational Kinetic Energy ► The energy of rotating objects Ek(rot) Ek ( rot) 1 2 Iw 2 Rolling Down Slopes ► Which will reach the bottom first?