2Rotation & Revolution Axis Rotation Revolution A straight line through which circular motion takes placeAll points on object orbit around the axisAll rotation/revolution requires an axisRotationObject rotating about an internal axisEx. Daily motion of the Earth, spiral footballRevolutionObject rotating about an external axisEx. Yearly motion of the earth
3How do we describe how fast something is rotating?? Speeds for objects in a straight line are called linear (or tangential) speeds,Linear speeds are a rate at which an object covers a certain distance (v =d/t)Ex. Unit – m/s , km/hr , mphCan’t express speeds of rotation with a linear speed,b/c objects at different points on the rotating object have different linear speedsRotational speed (ω)Expresses the rate at which an object rotates through a portion of a circle ( an angle)Ex. Unit RPM’s
4Below, a record spinning on a axis through its center (black dot) Faster linear speed, Star or Smiley??Smiley, travels a greater distance for eachFull spin.Faster rotational speed, Star or smiley??Both the same, b/c entire record is rotating at the same rate
5Are all people on Earth moving at the same speed?? Earth is rotating about an axis through its polesAre some of us moving with a greater LINEAR SPEED than others??Yes, closer to the Equator, the faster you are moving…. Closer to poles, the slower you are movingAre some of us moving with a greater ROTATIONAL SPEED than others??No, all people on earth have same rotational speed, because Earth is spinning at the same rate everywhere
6Rotational Inertia(I) AKA (not really but could be) Rotational MassResistance to change in rotational motionObjects that are rotating about an axis tend to stay rotating, objects not rotating tend to remain at rest, unless an outside torque is appliedA torque is required to change the status of an object’s rotationIt’s the rotational equivalent to mass,Harder to give an rotational acc. to an object w/ a larger I
7Rotational Inertia (cont.) Some objects have more rotational inertia than othersObjects with mass closer to axis of rotation are easier to rotate, b/c it they have less rotational inertiaIf the mass is farther away from the axis, then object will have more rotational inertia, and will therefore be harder to rotate
8Why does a tightrope walker carry a long pole? The pole is usually fairly heavy and by carrying it, he creates a lot of mass far away from the axis of rotationincreases in rotational inertia makes it harder for him to rotate/tip over
12The big idea Rotational Inertia depends on mass and radius If either one of these is large, then rotational inertia is large, and object will be harder to rotateDifferent types of objects have different equations for rotational inertiaBut all equations have m and r2 in them.
16TorqueCauses rotation, more specifically causes changes in rotationIts like the quantity Force but for rotationTorque (τ) = Force (F) x Lever Arm (d)Torque = F x dLever arm (d) - distance from axis of rotation that the F is appliedThe more torque the faster something will rotateView from above of Doors seen below……….F F FGood, long lever armNot as Good, shorter lever armVery Bad, no lever armddd
17No Force that is acting directly toward the axis, or directly away from it, can cause a torque NO TORQUE, Force must be perpendicular to the radius to cause a rotation
18Balanced TorquesIf more than one torque is acting on an object, the torques must be balanced on either side of the axis of rotation in order to be in rotational equilibrium (not rotating)In picture, axis is the triangle, Forces on either side of axis are not balanced…. BUT Torques are balanced.Rotational Equilibrium Net torque = 0Boy - Torque = 500 N x 1.5 m = 750 N*mGirl - Torque = 250 N x 3 m = 750 N*mSo teeter-totter is balanced!!(Aka in Equilibrium)In this case the forcescausing torque or the children’sWeight
19Below weights hanging on a meter stick Below weights hanging on a meter stick. Meter stick is suspended from the 50 cm mark. What is the weight of the first block, if the meter stick is balanced??If balanced that means that Torques on either side of Axis are balanced (hint-50 cm mark is axis)20 N block Torque = F x d = 20 N x 30 cm = 600Unknown block -- Torque = F x d = ? x 40 cm = 600So solve for ? By dividing 600 by 40 And you get 15 N!!!Dist. From axisDist. From axis? =15 N
20What does COG have to do with Torque?? Forces applied directly to the COG, have no lever arm….. And therefore produce no Torque…. Meaning no rotationAnother Football related exampleHow do you kick a football so it rotates end over end??
22Center of Gravity (COG) Definition--The Point located at an object’s average position of the weightIn other words…. The center of an object’s weightSymmetrical object’s, like a baseball the C of G would be in the exact center of objectHowever other oddly shaped objects will find COG in any number of positions, depending on weight distributionCOG
23C.O.G.When objects rotate freely they must rotate about an axis through the COGBasically treat the object as if all its weight is concentrated at that one pt.In class demos…
24C.O.G. --BalancingFor an object to balance, and not topple… support must be directly below C.O.G.
25Where C.O.G. is locatedGenerally found in the middle of all the weight…Does not even have to be within, the object itselfEx. boomerangWill be located toward one side of an object where most of its mass is focused…Ex. WeeblesCOGgravity
26Weebles Wobble, but they don’t fall down??? Weebles have very low COGWhenever rolling it will roll to a stop when its COG is as low as possibleThis occurs when it is standing uprightAlso occurs for inflatable toy clownsObjects with a low COG are less likely to topple because of this principleHigher COG is, the easier to topple
27Balancing StuffAgain, all that has to happen to balance, is for a support to be directly beneath COG
28Advantage of low COG Athletic advantages wrestling—harder to takedownFootball – “ “ “Both easier to drive power through their legsSUV’s …. Tip over all the time b/c COG is too highESUVEEFarmer’s tractorsMuch more control in allvehicles w/ low COG
29Deadliest CatchPots on deck and freezing ice make boat top heavy… more likely to roll and sinkBallast tanks at bottom help lower boat’s COG
32Humans - Where is our COG? Just below our belly buttonNotice, support always below COGBipedalism??Only mammals w/ this ability to walk on 2 legsBecause of Evolution and how our legs changed to balance between steps is why we are only mammals to walk
33Because our legs/hips evolved so that our support base (feet) were close together allows us to be bipedalApes and our early ancestors hips were constructed differently with a wide set base.Impossible to walk bipedalHip protruding from joint….Creates inward angled femurs…Which makes feet close together….Providing a stable/efficient base for walking upright
35Picking up Chair Demo Boys vs. Girls Why girls can do this but boys can’t??Different weight distribution of body types
36Centripetal ForceWhen driving in a circle, in what direction is a force acting on you?Pushing you outward from the circle, or inward?If you are swinging a yo-yo in a circle, and the string breaks…. What path does the yo – yo take??Ans Inwards, toward the center of the circleAns -- yo- yo goes in a path tangent to the circleHOWEVER, People commonly think there is a force pushing you out from the circleFeels like you are being pushed outwardExample ….. The Rotor- amusement park ride, a centrifuge, CD on your dashboard moving to the right when your turning leftWhy is this???
37The RotorPeople Stand with backs against wall of a large cylinder, cylinder then starts spinning, and people are seemingly pushed against the wall, then floor drops, and people are stuck against the wall.
38Centripetal Force Centripetal means “center- Seeking” Force pushes you toward the center of the circleIs the force that keeps youmoving in a circle, andkeeps your inertia fromtaking you in a straight lineCentripetal Force is affected by.. Mass (m),linear speed (vt),and radius (r)
39Centripetal ForceInertia wants to take objects in a tangent line, to the circular pathInertia is why you feel like your being pushed outwardThis outward pushing is sometimes called the Centrifugal Forcebut it is not actually a force, is only inertiaEvery object that moves in circular motion must experience a centripetal force from somewhere
40So why is there no Force pushing you out from the circle?? A force does not cause this…… your INERTIA does!!Inertia makes you want to stay in a straight line, and by going in a circle, you are fighting your own inertiaThis is how Rotor works, and why CD on dashboard happensThe only actual force acting on you is theCentripetal Force
41Centrifugal force Spin cycle in laundry Phone sliding off dashboard Dog shake
42Videos “G-Forces” NASA Centrifuge Centrifuge Training 9G test run Gross (negative G’s)Another 9 G test run
43Angular Momentum (L) L = Iω “inertia of rotation” Ang. Momentum= Rotational Inertia X Rotational SpeedL = IωLike normal momentum, but exclusively for rotation
44Conservation of Angular Momentum If no outside torque is being applied, then total angular momentum in a system must stay the sameThis means, if you decrease radius, you increase rotational speedIncrease radius, then rotational speed decreasesI – represents rotational inertiaω -represents angular speed
45Direction of Angular momentum Both magnitude and direction of angular momentum needs to be conservedThis means that an object that is spinning is much more stable than one that’s not because the direction of “L” must stay conserved too!Direction of ‘L’ , is defined by the right-hand ruleRight Hand Rule- curl fingers of your right hand in direction of rotation and your thumb will point to the direction of angular momentumBecause of this rotating objects are more stable because spinning objects need to conserve this directionGyroscopesBicycle wheel --- stays upright when spinning but flalls down when its notSpiral footballSpinning baseball vs. knuckleball
46Sports Connection… Ice skating Skater starts out in slow spin with arms and legs outSkater pulls arms and legs in tight to bodySkater is then spinning much fast (higher rotational speed)Gymnastics (pummel horse or floor routine)Small radius to achieve fast rotational speed during moves, increase radius when low rotational speed is desired (during landing)
47Do cats violate physical law? VideocatsNo rotate their tail one way, so that their body rotates the other so that their feet are facing the ground and they land on their feet.This combined with their flexibility all them to almost always land on their feet
49Universe ConnectionRotating star shrinks radius…. What happens to rotational speed??Goes way up….. Spins very fastRotating star explodes outward…. What happens to rotational speed??Goes way down … spins much slower