Circular Motion Chapter 9

Rotation and Revolution WHAT IS THE DIFFERENCE BETWEEN THE TWO? ROTATION – WHEN AN OBJECT TURNS ABOUT AN INTERNAL AXIS EX: WHEEL, CARNIVAL RIDE, EARTH ROTATES ON ITS AXIS OR “SPINS” REVOLUTION – WHEN AN OBJECT TURNS ABOUT AN EXTERNAL AXIS EX: EARTH REVOLVES AROUND THE SUN

TANGENTIAL SPEED THE SPEED OF SOMETHING MOVING ALONG A CIRCULAR PATH IS CALLED TANGENTIAL SPEED. BECAUSE THE DIRECTION OF MOTION IS ALWAYS TANGENT TO THE CIRCLE. FOR CIRCULAR MOTION, LINEAR AND TANGENTIAL SPEED ARE THE SAME THING.

QUESTION HOW DOES TANGENTIAL SPEED COMPARE TO THE ANGULAR VELOCITY OR ROTATIONAL SPEED?

ANSWER THE TANGENTIAL SPEED IS FASTER THE FARTHER FROM THE AXIS IT IS MEASURED BECAUSE IT MOVES A GREATER DISTANCE IN THE SAME AMOUNT OF TIME. A B

WHERE WILL “B” BE WHEN “A” COMPLETES A ROTATION? WHICH MOVES FASTEST? A B

ROTATIONAL SPEED ROTATIONAL SPEED – (ANGULAR SPEED) THE NUMBER OF ROTATIONS PER UNIT OF TIME. DIFFERENT FROM LINEAR SPEED – THE DISTANCE MOVED PER UNIT OF TIME. TANGENTIAL SPEED ~ RADIAL DISTANCE X ROTATIONAL SPEED

SUMMARY ANY RIDGIDLY ROTATING SYSTEM – ALL PARTS HAVE THE SAME ROTATIONAL SPEED, BUT THE TANGENTIAL SPEED WILL VARY ACCORDING TO THE DISTANCE FROM THE AXIS OF ROTATION.

QUESTION WHICH PART OF EARTH’S SURFACE HAS THE GREATEST ROTATIONAL SPEED ABOUT EARTH’S AXIS? ALL PARTS HAVE THE SAME SPEED. WHICH PART HAS THE GREATEST LINEAR SPEED RELATIVE TO EARTH’S AXIS? THE EQUATORIAL REGION HAS THE GREATEST LINEAR SPEED BECAUSE IT IS FARTHEST FROM THE AXIS.

QUESTIONS TRAINS RIDE ON A PAIR OF TRACKS. FOR STRAIGHT-LINE MOTION, BOTH TRACKS ARE THE SAME LENGTH. BUT WHICH TRACK IS LONGER FOR A CURVE, THE ONE ON THE OUTSIDE OR THE ONE ON THE INSIDE OF THE CURVE? THE OUTSIDE TRACK IS LONGER, JUST AS A CIRCLE WITH A GREATER RADIUS HAS A LONGER CIRCUMFERENCE.

EQUATIONS SOLVING FOR TANGENTIAL SPEED “V” IS TANGENTIAL SPEED SPEED = 2π(RADIUS) PERIOD V= 2π(r) T T – PERIOD – THE TIME IT TAKES TO COMPLETE ONE REVOLUTION.

FREQUENCY AND PERIOD FREQUENCY – THE NUMBER OF ROTATIONS OR REVOLUTIONS PER UNIT OF TIME PERIOD AND FREQUENCY ARE RECIPRICALS OF EACH OTHER T = 1/f PERIOD=1/FREQUENCY F = 1/T FREQUENCY=1/PERIOD UNIT IS HERTZ = 1/S

PRACTICE AFTER CLOSING A DEAL WITH A CLIENT, KENT LEANS BACK IN HIS SWIVEL CHAIR AND SPINS AROUND WITH A FREQUENCY OF 0.5 Hz. WHAT IS KENT’S PERIOD OF SPIN? T = 1/ 0.5 Hz = 2s

CENTRIPETAL MEANS CENTER SEEKING TOWARD THE CENTER

CENTRIPETAL FORCE ANY FORCE THAT CAUSES AN OBJECT TO FOLLOW A CIRCULAR PATH. IT IS NOT A NEW FORCE ANY FORCE DIRECTED PERPENDICULAR TO THE PATH OF A MOVING OBJECT CAUSING IT TO MOVE IN A CIRCULAR FASHION.

CENTRIPETAL FORCE DIAGRAM DIRECTION OF FORCE DIRECTION OF MOTION

QUESTION WHAT PROVIDES THE CENTRIPETAL FORCE FOR THE CAR NOT TO SKID OUT OF THE CURVE? FRICTION – NOT ENOUGH FRICTION AND THE CAR SLIDES.

CENTRIFUGAL FORCE NOT REAL MEANS CENTER FLEEING THERE IS NO FORCE PULLING OUT ON THE OBJECT. IF YOU SPIN WILLARD AROUND AND THE STRING BREAKS HE WILL FLY OFF IN A PATH TANGENT TO THE CIRCLE DUE TO INERTIA OF MOTION.

INERTIA THE RESISTANCE OF AN OBJECT TO CHANGE ITS MOTION WILLARD IS PULLING ON THE STRING BUT THERE IS NO OUTWARD FORCE ON WILLARD. THE CENTRIFUGAL FORCE EFFECT IS CAUSED BY INERTIA.

ARTIFICAL GRAVITY PRODUCED IN ROTATING SYSTEMS BY THE CENTRIFUGAL FORCE EFFECT. FORCES ACT IN PAIRS AND CENTRIFUGAL FORCE HAS NO PAIRED PARTNER BECAUSE OF THIS SCIENTISTS REFER TO IT AS A FICTITIOUS FORCE.

SPINNING WHEEL OCCUPANTS INSIDE THE WHEEL EXPERIENCE “CENTRIFUGAL FORCE” THAT FEELS LIKE GRAVITY WHEN THE WHEEL SPINS. UP IS TOWARD THE AXIS OF ROTATION DOWN IS RADIALLY OUTWARD

ACTION/REACTION THE FLOOR PRESSES AGAINST THE OCCUPANT(ACTION) THE OCCUPANT PRESSES BACK (REACTION) THE ONLY FORCE EXERTED ON THE MAN IS BY THE FLOOR AND IT IS DIRECTED TOWARD THE CENTER AND IS CALLED CENTRIPETAL FORCE.

HOW BIG DOES IT HAVE TO BE? SMALL DIAMETER STRUCTURES HAVE TO ROTATE FASTER THAN LARGE DIAMETER STRUCTURES TO PRODUCE 1 g WHAT IS 1 g? DO YOU FEEL THIS INFORMATION MAY BE IMPORTANT TO THE FUTURE?

EQUATION CENTRIPETAL ACCELERATION = LINEAR SPEED2/ RADIUS αc=v2/r Fc = m αc=mv2/r