OBJECTIVE:  

1) I will be able to demonstrate that the direction of a particle in circular motion is towards the center of that path after today's class.

WORDS FOR TODAY:

• centrifugal motion (inaccurate)
• centripetal motion

WORK O' THE DAY: 

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The correct term to describe both the acceleration and the forces involved for an object moving in circular motion is CENTRIPETAL MOTION/CENTRIPETAL FORCE (methinks that comes to us from the Latin meaning "Center - Seeking").

PLEASE, PLEASE, PLEASE purge the term centrifugal from your conscience... that is NOT accurate.

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Most textbooks do a crummy job of explaining centripetal motion. It can be a whole lot easier if you keep the following points in mind:

There is not such thing as a centripetal force.

Honest, there is no special force that flashes into existence when an object is moving in a circle... really. However, there is ALWAYS a source of the force that is pulling the object towards its center.

Consider a satellite moving in orbit around the Earth -- let's take a Goldilocks look at that situation (which is surprisingly common in physics and astronomy by the way):

• If the satellite moves too fast, it flies off into space
• If the satellite moves too slowly it gets pulled to Earth
• If the satellite's velocity is JUST right it stays in orbit.

There is a relationship between the speed in which an object is moving in circular motion to the force that is pulling on it:

F_c = mv²/r

Similarly the acceleration of that object is found by:

A_c = v²/r

Soooo.... a better way to discuss centripetal acceleration is to say:

"How fast must an object travel in a circular fashion in order NOT to be pulled to the center and NOT to fly off into space."

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1) A pendant on the end of a chain that you are swinging around in your hand

2) The Moon revolving (please don't say rotating, that's something different) around the Earth

3) A car traveling in a circular path as it exits a freeway off-ramp (careful!)

Talk with your group to determine the FORCE (or forces) exerted in each situation that forces each of those objects to move in a circular path?

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Answers:

1) A pendant on the end of a chain that you are swinging around in your hand (Force exerted by your muscles on the chain pulling towards the center)

2) The Moon revolving (please don't say rotating, that's something different) around the Earth (The gravitational force exerted by the Earth on the moon trying to pull the moon towards the Earth)

3) A car traveling in a circular path as it exits a freeway off-ramp (because the road is banked, we have both x and y components of the normal force as well as the frictional force between the tires and the road)

Notice that in EACH case, the force is just a good ol' generic force that we've already discussed in previous chapters. The key here is that in THESE cases, that force constrains the object to move in a circular path.

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What happens if that force is suddenly interrupted or discontinued? What path will the object take?? (take in your groups please)

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Now let's take a few moments to learn about terms in circular motion:

Please Read 4.4 and review the analysis model:

Be prepared to EXPLAIN (dare I say, without notes?) why some professor-types teach the centripetal force is a "Phantom" force.

• Centripetal acceleration (A_c)
• Centripetal Force (F_c)

Take a few moments to read 4.5

HOMEWORK:

33, 36, 40 & 41