Important situations in circular motion

When accelerating, the feeling you have is opposite the acceleration This is why it feels like there is centrifugal acceleration when it’s really centripetal acceleration.

Centripetal force is the general name given to the inward force The centripetal force IS THE Tension The centripetal force IS THE Friction The centripetal force IS THE Force of Gravity

Notice the v and a are at right angles This is always true for uniform circular motion

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

This is the view from above for a board with a ball on it with and without a wall This is the view from above for a board with a ball on it with and without a wall As the cart turns, what happens to the ball? As the cart turns, what happens to the ball? A force toward the center is necessary to cause turning.

How much acceleration? As you may have seen in the lab, centripetal acceleration depends on two factors: As you may have seen in the lab, centripetal acceleration depends on 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 acceleration can be determined by the equation: The magnitude of centripetal acceleration can be determined by the equation: a c = v 2 /r

Other important measurements Period (T): The time it takes for one complete rotation (measured in seconds) Period (T): The time it takes for one complete rotation (measured in seconds) Frequency (f): How many complete rotations happen per second (measured in Hertz; 1 Hz = 1 rotation per second) Frequency (f): How many complete rotations happen per second (measured in Hertz; 1 Hz = 1 rotation per second) We could also calculate a c using period or frequency (however, we won’t in this class) We could also calculate a c using period or frequency (however, we won’t in this class)

Free Body for anything circling vertically Like a bucket of water Like a bucket of water Both forces are down at the top Both 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 line Nope, inertia keeps the water moving in a straight line The combined (net) forces are causing centripetal acceleration – making it turn The combined (net) forces are causing centripetal acceleration – making it turn Acceleration is not the same as motion! (recall braking car – a is backwards but car moves forward) Acceleration is not the same as motion! (recall braking car – a is backwards but car moves forward)

As the coaster goes around the loop the force for turning, the track, must be into the center of the loop. As the coaster goes around the loop the force for turning, the track, must 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 is the normal force? At the top of the loop what direction is the normal force? Down Down Both gravity and Both gravity and the normal are directed downward

Any time there is turning There must be an unbalanced net force causing an acceleration.

Remember Newton’s 2 nd Law!! F = ma F = ma For centripetal force, F net = ma c For centripetal force, F net = ma c

Orbiting We know orbiting satellites have centripetal force What is the centripetal force here? Force of gravity Is gravity here F g =mg=m*9.8 m/s 2 ? NO! Why not? Too far from Earth for g=9.8m/s 2 Is g = 0?

NO! g≠0 ever! You are in free fall, your “weightlessness” is due to lack of a normal force You are in free fall, your “weightlessness” is due to lack of a normal force Your inertia moves you tangent to the orbital path, but the gravity pulls you in Your inertia moves you tangent to the orbital path, but the gravity pulls you in So how do you calculate the F g ? So how do you calculate the F g ?

Law of Universal Gravitation Legend has it that Newton thought “an apple falls to the Earth because of the force of gravity. At what distance does the force stop pulling? Does the force of gravity pull on the moon?” Legend has it that Newton thought “an apple falls to the Earth because of the force of gravity. At what distance does the force stop pulling? Does the force of gravity pull on the moon?” Eventually he realized that there must be a gravitational force between every pair of objects Eventually he realized that there must be a gravitational force between every pair of objects The amount of force depended on the masses of the objects and the distance between them The amount of force depended on the masses of the objects and the distance between them

Law of Universal Gravitation

For an orbiting object  F=ma  F=ma  F= F g = ma gravity is the only force  F= F g = ma gravity is the only force F g = Gm 1 m 2 /r 2 = ma F g = Gm 1 m 2 /r 2 = ma Gm 1 m 2 /r 2 = ma = mv 2 /r Gm 1 m 2 /r 2 = ma = mv 2 /r Same r’s so one cancels Same r’s so one cancels One m is the mass of the object; it cancels One m is the mass of the object; it cancels So all you need is the radius to find the velocity! So all you need is the radius to find the velocity! Gm 1 m earth /r 2 = mv 2 /r so Gm 2 /r = v 2 Gm 1 m earth /r 2 = mv 2 /r so Gm 2 /r = v 2

Try some multiple choice at general site general site Specific to Ch. 5 self assessment Specific to Ch. 5 self assessment college/cutnell/ /sat/media/html/sa t_c05/sat_c05.htm