AP Physics Circular Motion

Period

how much time it takes for the object to complete one circle

• t and seconds

Frequency

how many circles an object completes in one second

• f and circles per second (Hz)

Period and Frequency are .

reciprocals--> T = 1/f and f= 1/T

Every circle has a _.

radius (R in meters)

Arc Length

a portion of the circumference of a circle (d for distance)

Arc angle

the opening between two lines that meet at a point

• express in radians (90 degrees is pi/2)

Linear speed

how many meters of arc length the object travels around the circle every second

• v in m/s

• same as normal speed for circles

Angular speed (w)

how many radians of arc angle the object travels around the circle every second

• radians per second

Calculating linear speed

Circumference and period--> v = 2pir/T or 2pirf

• circumeferece = 2pir

• period = T

Calculating angular speed

angle over time

• 2pi radians/T —> or w = 2pif

Relationship between v and w

s = R0 --> divide by time --> s/t = R(0/t)

• s/t = linear speed (v)

• 0/t = angular speed (w)

• v = Rw

Uniform Circular Motion

• the object moves along a path that is part of a circle

• does not need to be full circle

• radius is constant

• linear and angular speed are constant

Centripetal Acceleration

constant acceleration towards the center of a circle

• v^2/R or w²R

Centripetal force

describes any force that points toward the center of the circle (points away--> negative)

• gravity on earth

Tangential Acceleration

the component of the acceleration vector that is parallel to the velocity vector, tangent to the path

Tangential Force

describes any force that is parallel to the velocity and tangent to the path

Centripetal and Tangential Accel.

• acceleration can be broken into two components (parallel tang, perpendicular centripetal

• tangential: parallel to the velocity vector, changes speed of object

• centripetal: perpendicular to the velocity vector, towards the circle, changes the direction of the object—> creating the curved path

Angular Acceleration--> What if w changes?

when the angular speed (w) changes

• change in angular speed/change in time = a (alpha)

• rad/s²

How alpha (a) relates to tangential acceleration

• s = 0r --> divide both sides by t--> s/t = 0/t

• s/t=v

• 0/t=w

• v=wr—> divide by t again —> v/t = tangential acceleration

• w/t = angular acceleration

• at = ar

Rotational Kinematics Equations

Constant angular velocity: theta = wt + theta initial

Constant Angular Acceleration:

• w = at + w0

• theta = 1/2at²+w0t+0²

• w² = w0² + 2a0

Inverse - Square Law

principle that governs some fundamental forces where the strength of the force decreases as the square of the distance between objects

Law of Universal Gravitation

equation for the force of gravity that works for all the objets in the universe, and not just Earth (Newton and Johannes Kepler)

Fg = GmM/r^2

Distance between the objects m and M is r

• g = Universal Gravitational Constant or 6.67 × 10^-11

• force of gravity is directly proportional to each mass

• force of gravity has an inverse square relationship with distance r

Gravitational Field

a force field that exists in the space around every mass or group of masses

• go towards the earth

• if two objects have the same force of gravity, we can set the equations towards each other (fg = GmM/r² and fg = mg)

• mg = GmM/r² —> g = GM/r²

Density

mass/volume

• suppose a new planet has twice the radius of Earth, what would the gravity be? —> relies on whether the masses or densities are the same as the Earth

• if the mass is the same —> g = GM/r², ¼ of the gravitational field

• if the density is the same —> m/v = d—> dv = m —> if the radius has doubled, the mass had to have doubled (2x)