AP Physics C: Circular Motion and Gravity

speed

scalar

velocity

vector

on a plate, the ball’s instantaneous velocity

straight line tangent to the curve

rolling a ball at a constant speed around on the plate, is it accelerating?

yes because it’s changing direction

A=(change of v)/t

A force perpendicular to an objects motion….

…will cause it to change direction not speed

Period (T)

The time it takes for something to complete 1 entire cycle/revolution

Reciprocal to frequency

Frequency (f)

The number of cycles /revolutions completed by an object in a second

Reciprocal to period

Equation for Period

T = 1/f

Speed equation

V=d/t = 2(pi)R/T = 2(pi)Rf

V is what to the curve?

Tangent

Centripetal acceleration

Represents the rate of direction change (turning rate)

Always points into the circle traveled by the object

Only changes direction of velocity, it doesn’t speed up the object or slow down the object

Equation for centripetal acceleration

Ac. V² / R

v= speed of object moving in circle

R=radius of circle the object travels in

UCM

Uniform circular motion

Constant speed

Only Ac, no Atan

Relationship between v and Ac

V:Ac

Direct relationship

Relationship between R and Ac

Opposite

R would decrease as Ac increases

Inverse relationship

What can rapid turn rate be from

High speed, sharp turns, or both

If you slow down/speed up, Atan and Ac will…

…will be present

Force Fg

Directly proportional to the masses (M + m) and is inversely proportional to the square of the center to center distance R between the objects

Newtons universal force of gravity

All masses M in the universe pull/attract every other mass m with gravitational force Fg

Relationships btwn M1M2 and Fg

Proportional

Direct relationship

Relationship btwn R and Fg

Inverse relationship

Gravitational force

FG = Gm1(m2) / R²

R= the center-to-center distance btwn the two masses M and m

little g

Acceleration due to gravity (gravitational field)

Masses create a gravitational field g around them

The filled g exerts grav force on other masses in its field

Method 1 of calculating g

Fg=mg

Fg=Gmm2/R²

g=GMp/R²

Method 2 for calculating g

g=Fg/m

m=mass placed in the gravitational field

Fg= gravitational force exerted on mass m

Density

p=m/v

m=pv

Volume of a sphere

V=4/3(pi)R³

Gravitational orbit

When an astronomical object (like a planet) orbits another Astro. Obj , we say it is in a gravitational orbit

If the orbit is a circle we can use the form for Ac to relate the speed, radius of orbit, and mass

Formula for gravitational orbit

Vo=(square root) GMp/R

Gravitational field due to a uniform solid sphere

max strength of the Fg is right at the surface of the planet

As you leave a planet, g decreases w 1/R²

Outside the sphere, it is the same as if all of the objet’s mass were concentrated at its center of mass

Tunneling into the center of a planet, g wold decrease linearly

Grav field due to a uniform thin, hollow shell

g=0 inside

G=GMp/R²

Gravitational force on an object inside a solid sphere

an object inside a solid sphere of uniform density experiences a new gravitational force from only a partial

Mass of the sphere

Fg=Gm1m2/R²

Martial =p4/3(pi)(rpartial)³

Period equation

T= time/number of cycles

frequency equation

f=number of cycles/time

Force of friction

Fg (less than or equal to) (mew)FN