Important Important situations in situations in

circular motioncircular motion

When accelerating, the When accelerating, the feeling you have is opposite feeling you have is opposite

the accelerationthe acceleration

This is why it feels like there is centrifugal acceleration when it’s really centripetal acceleration.

Centripetal force is the Centripetal force is the general name given to the general name given to the

inward forceinward force

The centripetal force IS THETension

The centripetal force IS THEFriction

The centripetal force IS THE

Force of Gravity

Notice the v and a are at Notice the v and a are at right anglesright angles

This is always true for uniform circular motion

Newton’s first law dictates that the Newton’s first law dictates that the object will remain in straight line object will remain in straight line motion until a force cause turningmotion until a force cause turning

This is the view from above for a This is the view from above for a board with a ball on it with and board with a ball on it with and without a wallwithout a wall

As the cart turns, what happens to As the cart turns, what happens to the ball?the ball?

A force toward the center is necessary to cause turning.

How much acceleration?How much acceleration?

As you may have seen in the lab, As you may have seen in the lab, centripetal acceleration depends on centripetal acceleration depends on two factors:two factors: The speed of the object (v)The speed of the object (v) The radius of the circular motion (r)The radius of the circular motion (r)

The magnitude of centripetal The magnitude of centripetal acceleration can be determined by acceleration can be determined by the equation:the equation:

aacc = v = v22/r/r

Other important Other important measurementsmeasurements

Period (T):Period (T): The time it takes for one The time it takes for one complete rotation (measured in complete rotation (measured in seconds)seconds)

Frequency (f): Frequency (f): How many complete How many complete rotations happen per second (measured rotations happen per second (measured in Hertz; 1 Hz = 1 rotation per second)in Hertz; 1 Hz = 1 rotation per second)

We could also calculate aWe could also calculate acc using period using period or frequency (however, we won’t in this or frequency (however, we won’t in this class)class)

Free Body for anything circling Free Body for anything circling verticallyvertically

Like a bucket of waterLike a bucket of water Both forces are down at the topBoth forces are down at the top So doesn’t that mean the water will surely fall out?So doesn’t that mean the water will surely fall out? Nope, inertia keeps the water moving in a straight Nope, inertia keeps the water moving in a straight

lineline The combined (net) forces are causing centripetal The combined (net) forces are causing centripetal

acceleration – making it turnacceleration – making it turn Acceleration is not the same as motion! (recall Acceleration is not the same as motion! (recall

braking car – a is backwards but car moves braking car – a is backwards but car moves forward)forward)

As the coaster goes around the loop As the coaster goes around the loop the force for turning, the track, must the force for turning, the track, must be into the center of the loop. be into the center of the loop.

What is the force from the track? What is the force from the track? The normal force!!The normal force!!

At the top of the loop what direction At the top of the loop what direction is the normal force? is the normal force? DownDown Both gravity and Both gravity and

the normal are directedthe normal are directed

downwarddownward

Any time there is turningAny time there is turning

There must be an unbalanced net force causing an acceleration.

Remember Newton’s 2Remember Newton’s 2ndnd Law!!Law!!

F = maF = ma

For centripetal For centripetal force, Fforce, Fnetnet = ma = macc

OrbitingOrbitingWe know orbiting satellites have We know orbiting satellites have

centripetal forcecentripetal force

What is the centripetal force here?What is the centripetal force here?

Force of gravityForce of gravity

Is gravity here FIs gravity here Fgg=mg=m*9.8 m/s=mg=m*9.8 m/s22??

NO!NO!

Why not?Why not?

Too far from Earth for g=9.8m/sToo far from Earth for g=9.8m/s22

Is g = 0?Is g = 0?

NO! gNO! g≠0 ever!≠0 ever! You are in free fall, your You are in free fall, your

“weightlessness” is due to lack of a “weightlessness” is due to lack of a normal forcenormal force

Your inertia moves you tangent to Your inertia moves you tangent to the orbital path, but the gravity pulls the orbital path, but the gravity pulls you inyou in

So how do you calculate the FSo how do you calculate the Fgg??

Law of Universal Law of Universal GravitationGravitation

Legend has it that Newton thought “an Legend has it that Newton thought “an apple falls to the Earth because of the apple falls to the Earth because of the force of gravity. At what distance does force of gravity. At what distance does the force stop pulling? Does the force of the force stop pulling? Does the force of gravity pull on the moon?”gravity pull on the moon?”

Eventually he realized that there must be Eventually he realized that there must be a gravitational force between every pair a gravitational force between every pair of objectsof objects

The amount of force depended on the The amount of force depended on the masses of the objects and the distance masses of the objects and the distance between thembetween them

Law of Universal Law of Universal GravitationGravitation

For an orbiting objectFor an orbiting object

F=maF=ma F= FF= Fgg = ma gravity is the only force = ma gravity is the only force

FFgg = Gm = Gm11mm22/r/r22 = ma = ma

GmGm11mm22/r/r22 = ma = mv = ma = mv22/r/r Same r’s so one cancelsSame r’s so one cancels One m is the mass of the object; it One m is the mass of the object; it

cancelscancels So all you need is the radius to find the So all you need is the radius to find the

velocity!velocity! GmGm11mmearthearth/r/r22 = mv = mv22/r so Gm/r so Gm22/r = v/r = v22

Try some multiple choice Try some multiple choice atat

www.wiley.com/college/cutnell general sitegeneral site

Specific to Ch. 5 self assessmentSpecific to Ch. 5 self assessment

http://http://www3.interscience.wiley.com:8100/www3.interscience.wiley.com:8100/legacy/college/cutnell/0471151831/legacy/college/cutnell/0471151831/sat/media/html/sat_c05/sat_c05.htmsat/media/html/sat_c05/sat_c05.htm