Circular Motion and rotating reference frames Circular Motion The Centrifugal Effect The Centripetal Force The Coriolis effect

The Centrifugal Effect D

D D

D D

Centrifugal effect vs. Centripetal Force There is nothing “forcing” the object to move “outward” – Centrifugal effect Something must make the driver (and the car) turn – Centripetal Force

Inertial, or Fictitious, forces From “bird’s eye view”, Newton’s laws work. From “Driver’s view”, they “don’t”. Driver interprets “movement” as coming from a “force”. Einstein called it an “inertial” force.

So what does the “bird” see? Something is making the driver, and car, turn. This is “the” Centripetal force. Better to say that “all of the forces provide the centripetal force”.

Centripetal Acceleration R 2 + (v Δt) 2 = (R + ½ a (Δt) 2 ) 2 => a = v 2 /R (if Δt small) v Δt R ½a(Δt) 2 R

Simple Numerical Examples  A 20 kg ball is attached to the end of a 4 meter long string. If the ball is rotated at 5 m/s, what it the tension in the strting?  The same ball is attached to a different, 3 meter long string which breaks if its tension exceeds 600 N. What is the maximum speed with which you can rotate the ball?

Real World examples All examples will be explained with diagrams on the board.  Coin on rotating disc  Amusement park ride “The rotor”, or “The hell- hole”.  Banked curves on roads; no friction.

Apparent Weight  Apparent weight at the top of Ferris wheel  Apparent wt at the bottom of Ferris wheel  More general than this...  Apollo 13 movie

Another “inertial” force Let’s shoot an object from the equator towards the North Pole, using our “eye” to aim it... First without earth’s rotation, then including the rotation. Take careful notes so that you understand the pictures!!

Coriolis effect With respect to Earth’s rotation, noticeable only for large distances, high speeds, long times. Sorry Simpsons, X-Files, basketball player, English navy Hard to isolate in lab without large angular speed. (ω earth = 7.27 × rad/sec)

More Coriolis Although we can make other things rotate and see the effect...