1. Chp 9-11 Rotational Motion

2. Some Vocab Terms  Axis – the straight line around which rotation takes place  Rotation – when an object spins around an axis located inside the body (ex. Ice skater spinning)  Revolution – when an object spins around an axis located outside the body (ex. Planets orbit the sun)

3. Speed of Circular Motion  # revolutions = Rotational Speed time  Tangential speed - the speed at the outside edge of revolution  Gets larger as the radius increases  = radius x rotational speed ** For the same rotating system, all objects have the same rotational speed, but the further they are from the axis, the faster the tangential speed becomes.

4. Forces of Circular Motion  Centripetal force – a center directed force that causes circular motion  Always directed at a right angle to the path of motion  Without it, no circular motion would occur  Centrifugal force – an imaginary force that feels like it’s pushing you outward  Occurs because an object’s inertia wants to continue to follow the straight line path, but the centripetal force won’t allow it  Can be used to create artificial gravity

5. Some Formulas  V = 2  r t  T = 1 F  A c = v 2 r  F c = mv 2 r ** Because these are for circular motion, they are directed towards the center of the circular path of motion.

6. Center of Gravity  The point around which an object rotates.  It is near the geometric center if density is consistent.  It is the exact center if an object is symmetrical.  It can also be found by suspending the object from 2 different points and marking where the vertical lines intersect.  It can be located in empty space. (ex. The hole in a donut)

7. Motion and C.O.G.  Objects roll to allow c.o.g. to be as low as possible.  When an object is thrown, the c.o.g. follows a straight line path, and the rest of the object orbits that point.  If the c.o.g. moves beyond the support base of an object, it will topple over.

8. Differences in C.O.G.  A man’s c.o.g. is typically higher on their body than a woman’s.  Changing your body shape can change your c.o.g., and even move it outside your body. (ex. Athletes)  When an object is at rest materials will shift so that heaviest objects sink to the bottom to lower the c.o.g. of the whole. (ex. Sand in water)

9. Some Vocab  Unstable equilibrium – when an object is placed so that toppling would lower its c.o.g.  Stable equilibrium – when an object is placed so that toppling would raise its c.o.g.  Takes work to topple these objects. The more work it takes, the more stable the object.  Tall buildings often have part of their structure underground so c.o.g. is underground and the building would be unable to fall over intact.

10. Torque  A force that produces rotation.  Must be applied with leverage.  Must be off c.o.g.  The longer the lever arm, the less force required.  The more perpendicular the force, the less effort required.  If a counterclockwise torque is balanced by a clockwise torque, no rotation occurs.  T = F x lever arm

11. Rotational Inertia  Once an object starts rotating, it will continue to do so until an outside for stops it (just like any other kind of motion).  It depends on the mass involved and its distribution.  The greater the distance between the axis and the bulk of the mass, the harder to change rotation. (ex. Choking up on a bat)  So which rolls down the hill first, a solid disk or a hollow ring of the same mass and radius?  You can change your inertia by changing your body position.

12. Angular Momentum  AM = rotational inertia x rotational velocity OR  AM = mvr  A net external torque is required to change the AM.  This is why bikes are easier to balance when they are moving, they have AM.  AM is conserved, so if inertia is big, velocity is small and vice versa.  This is why skaters spin faster when they pull their arms in.