# Circular Motion CH. 8.

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Circular Motion CH. 8

Rotation & Revolution Axis Rotation Revolution
A straight line through which circular motion takes place All points on object orbit around the axis All rotation/revolution requires an axis Rotation Object rotating about an internal axis Ex. Daily motion of the Earth, spiral football Revolution Object rotating about an external axis Ex. Yearly motion of the earth

How 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 , mph Can’t express speeds of rotation with a linear speed, b/c objects at different points on the rotating object have different linear speeds Rotational speed (ω) Expresses the rate at which an object rotates through a portion of a circle ( an angle) Ex. Unit RPM’s

Below, a record spinning on a axis through its center (black dot)
Faster linear speed, Star or Smiley?? Smiley, travels a greater distance for each Full spin. Faster rotational speed, Star or smiley?? Both the same, b/c entire record is rotating at the same rate

Are all people on Earth moving at the same speed??
Earth is rotating about an axis through its poles Are 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 moving Are 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

Rotational Inertia(I)
AKA (not really but could be) Rotational Mass Resistance to change in rotational motion Objects that are rotating about an axis tend to stay rotating, objects not rotating tend to remain at rest, unless an outside torque is applied A torque is required to change the status of an object’s rotation It’s the rotational equivalent to mass, Harder to give an rotational acc. to an object w/ a larger I

Rotational Inertia (cont.)
Some objects have more rotational inertia than others Objects with mass closer to axis of rotation are easier to rotate, b/c it they have less rotational inertia If the mass is farther away from the axis, then object will have more rotational inertia, and will therefore be harder to rotate

Why 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 rotation increases in rotational inertia makes it harder for him to rotate/tip over

More tight rope walkers….
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Sports Connection Running Gymnastics/Diving
When you run you bend your legs to reduce your rotational inertia Gymnastics/Diving Pull body into tight ball to achieve fast rotation

Videos - Diver Spinning in zero Gravity

The 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 rotate Different types of objects have different equations for rotational inertia But all equations have m and r2 in them.

Rotational Mechanics

Torque Causes rotation, more specifically causes changes in rotation Its like the quantity Force but for rotation Torque (τ) = Force (F) x Lever Arm (d) Torque = F x d Lever arm (d) - distance from axis of rotation that the F is applied The more torque the faster something will rotate View from above of Doors seen below………. F F F Good, long lever arm Not as Good, shorter lever arm Very Bad, no lever arm d d d

No 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

Balanced Torques If 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 = 0 Boy - Torque = 500 N x 1.5 m = 750 N*m Girl - Torque = 250 N x 3 m = 750 N*m So teeter-totter is balanced!! (Aka in Equilibrium) In this case the forces causing torque or the children’s Weight

Below 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 = 600 Unknown block -- Torque = F x d = ? x 40 cm = 600 So solve for ? By dividing 600 by 40 And you get 15 N!!! Dist. From axis Dist. From axis ? =15 N

What does COG have to do with Torque??
Forces applied directly to the COG, have no lever arm….. And therefore produce no Torque…. Meaning no rotation Another Football related example How do you kick a football so it rotates end over end??

Hewitt Program

Center of Gravity (COG)
Definition--The Point located at an object’s average position of the weight In other words…. The center of an object’s weight Symmetrical object’s, like a baseball the C of G would be in the exact center of object However other oddly shaped objects will find COG in any number of positions, depending on weight distribution COG

C.O.G. When objects rotate freely they must rotate about an axis through the COG Basically treat the object as if all its weight is concentrated at that one pt. In class demos…

C.O.G. --Balancing For an object to balance, and not topple… support must be directly below C.O.G.

Where C.O.G. is located Generally found in the middle of all the weight… Does not even have to be within, the object itself Ex. boomerang Will be located toward one side of an object where most of its mass is focused… Ex. Weebles COG gravity

Weebles Wobble, but they don’t fall down???
Weebles have very low COG Whenever rolling it will roll to a stop when its COG is as low as possible This occurs when it is standing upright Also occurs for inflatable toy clowns Objects with a low COG are less likely to topple because of this principle Higher COG is, the easier to topple

Balancing Stuff Again, all that has to happen to balance, is for a support to be directly beneath COG

wrestling—harder to takedown Football – “ “ “ Both easier to drive power through their legs SUV’s …. Tip over all the time b/c COG is too high ESUVEE Farmer’s tractors Much more control in all vehicles w/ low COG

Deadliest Catch Pots on deck and freezing ice make boat top heavy… more likely to roll and sink Ballast tanks at bottom help lower boat’s COG

Animals Low COG High COG

T. Rex & Tails

Humans - Where is our COG?
Just below our belly button Notice, support always below COG Bipedalism?? Only mammals w/ this ability to walk on 2 legs Because of Evolution and how our legs changed to balance between steps is why we are only mammals to walk

Because our legs/hips evolved so that our support base (feet) were close together allows us to be bipedal Apes and our early ancestors hips were constructed differently with a wide set base. Impossible to walk bipedal Hip protruding from joint…. Creates inward angled femurs… Which makes feet close together…. Providing a stable/efficient base for walking upright

How to find COG….

Picking up Chair Demo Boys vs. Girls
Why girls can do this but boys can’t?? Different weight distribution of body types

Centripetal Force When 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 circle Ans -- yo- yo goes in a path tangent to the circle HOWEVER, People commonly think there is a force pushing you out from the circle Feels like you are being pushed outward Example ….. The Rotor- amusement park ride, a centrifuge, CD on your dashboard moving to the right when your turning left Why is this?? ?

The Rotor People 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.

Centripetal Force Centripetal means “center- Seeking”
Force pushes you toward the center of the circle Is the force that keeps you moving in a circle, and keeps your inertia from taking you in a straight line Centripetal Force is affected by.. Mass (m), linear speed (vt), and radius (r)

Centripetal Force Inertia wants to take objects in a tangent line, to the circular path Inertia is why you feel like your being pushed outward This outward pushing is sometimes called the Centrifugal Force but it is not actually a force, is only inertia Every object that moves in circular motion must experience a centripetal force from somewhere

So 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 inertia This is how Rotor works, and why CD on dashboard happens The only actual force acting on you is the Centripetal Force

Centrifugal force Spin cycle in laundry Phone sliding off dashboard
Dog shake

Videos “G-Forces” NASA Centrifuge Centrifuge Training 9G test run
Gross (negative G’s) Another 9 G test run

Angular Momentum (L) L = Iω “inertia of rotation”
Ang. Momentum= Rotational Inertia X Rotational Speed L = Iω Like normal momentum, but exclusively for rotation

Conservation of Angular Momentum
If no outside torque is being applied, then total angular momentum in a system must stay the same This means, if you decrease radius, you increase rotational speed Increase radius, then rotational speed decreases I – represents rotational inertia ω -represents angular speed

Direction of Angular momentum
Both magnitude and direction of angular momentum needs to be conserved This 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 rule Right Hand Rule- curl fingers of your right hand in direction of rotation and your thumb will point to the direction of angular momentum Because of this rotating objects are more stable because spinning objects need to conserve this direction Gyroscopes Bicycle wheel --- stays upright when spinning but flalls down when its not Spiral football Spinning baseball vs. knuckleball

Sports Connection… Ice skating
Skater starts out in slow spin with arms and legs out Skater pulls arms and legs in tight to body Skater 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)

Do cats violate physical law?
Video cats No 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