Advanced Physics

Chapter 5Circular Motion: Gravitation

Chapter 5: Circular Motion: Gravitation

5-1 Kinematics of Uniform Circular Motion5-2 Dynamics of Uniform Circular Motion5-3 Highway Curves, Banked and Unbanked5-4 Nonuniform Circular Motion5-6 Newton’s Law of Universal Gravitation5-7 Gravity near the Earth's Surface5-8 Satellites and “Weightlessness”5-10 Types of Forces in Nature

5-1 Kinematics of Uniform Circular Motion

Uniform Circular Motion

object that moves in a circle with constant speed

magnitude of velocity is constant but direction is changing

5-1 Kinematics of Uniform Circular Motion

Centripetal (radial) acceleration (ar or ac)

center-seeking acceleration

acceleration directed toward the center of the circle

velocity and acceleration vectors are perpendicular to each other

5-1 Kinematics of Uniform Circular Motion

Velocity v = d/t d = 2rso v = 2r/Twhere T = period of

revolution (sec)and f = frequency

(sec-1)T = 1/f

5-1 Kinematics of Uniform Circular Motion

Centripetal acceleration

aR = v2/r

aR = 42r/T2

5-2 Dynamics of Uniform Circular Motion

According to Newton’sSecond Law: Fnet = ma

FR = maR = mv2/r

net centripetal force (FR) must be directed toward center (why?)

centripetal force vs. centrifugal force

5-3 Highway Curves, Banked and Unbanked

When a car goes around a curve in the road what keeps it on the road?

When is the friction between the tires and the road greater, when they are rolling or sliding?

So to keep a car on the road on a curve we must……

5-3 Highway Curves, Banked and Unbanked

Banking a curve reduces skidding why?

Fn is at an angle toward the center of the curve

so a portion of the Fn goes into FR so the tires need to supply less frictional force to make up for the remaining FR needed

5-3 Highway Curves, Banked and UnbankedBanking angle of roadFnsin = mv2/r

since Fncos = mg then Fn = mg/cos

mg(sin /cos) = mv2/r

g(tan ) = v2/rtan = v2/rg so banking angle of road

doesn’t depend on m, just v,r and g

5-4 Nonuniform Circular Motion

For an object in UCM; the only acceleration is due to radial (centripetal) acceleration

aR is caused by what? Equation?But if the object in circular motion is

speeding up or slowing down there is another type of acceleration, tangential acceleration

5-4 Nonuniform Circular Motion

Tangential acceleration (atan)Acceleration caused by the

change in the magnitude of the velocity of an object moving in a circular path

atan = v/t

5-4 Nonuniform Circular Motion

Total vector acceleration (a)Acceleration caused by the change

in the magnitude and direction of the velocity of an object moving in a circular path

It is the sum of both the tangential and radial acceleration of an object

a = atan + aR

5-4 Nonuniform Circular Motion

Total vector acceleration (a)

a = atan + aR

The magnitude of a at any moment is:

a = (a2tan + a2

R)1/2

5-6 Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation

every particle in the Universe attracts every other particle with a force that is proportional to their masses and inversely proportional to the distance between them

5-6 Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation

the force of gravity acts along a line joining the two particles.

F = Gm1m2/d2

G = 6.67 x10 –11

Nm2/kg2

5-6 Newton’s Law of Universal Gravitation

Find the force of gravity between two electrons that are 2.3x10-2 nm apart

Answer: 1.05 x 10-49 N

5-7 Gravity near the Earth's Surface

Since the force of gravity is equal to the weight of an object…

Gmome/r2 = mogso….g = Gme/r2

so..gravity (g) doesn’t depend on the mass of the object, just G, me and r!

5-8 Satellites and “Weightlessness”

Why do satellites orbit the Earth?

How can a person orbiting the Earth experience “weightlessness”?

Many nasty effects of weightlessness on the body

5-8 Satellites and “Weightlessness”

What is the relationship between Fn, Fa, and Fg in the following situations?

stationaryaccelerating upaccelerating down in free-fall

5-10 Types of Forces in Nature

Four different fundamental forces:

gravitational force force between any two objects

electromagnet force force between any two charged

objects

strong nuclear force force that holds the nucleus together

weak nuclear force force involved in certain types of

nuclear decay

5-10 Types of Forces in Nature

What is GUT?