Chp 9-11 Rotational Motion

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)

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.

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

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.

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)

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.

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)

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.

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

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.

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.