Important Important situations in situations in circular motion circular motion
Jan 03, 2016
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
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