Circular Motion and rotating reference frames

Circular Motion

The Centrifugal Effect

The Centripetal Force

The Coriolis effect

The Centrifugal Effect

D

The Centrifugal Effect

D

D

The Centrifugal Effect

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

R2 + (v Δt)2 = (R + ½ a (Δt)2)2 =>

a = v2/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

An object’s true weight (W) is the force of gravity on an object. W = mg

An object’s apparent weight is the “weight measured on a scale” (so we’ll label it “S”)

If ∑F = 0, then S = W. Otherwise . . .??

What is your apparent weight in an elevator?

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. (ωearth = 7.27 × 10-5 rad/sec)

More Coriolis

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