Uniform Constant Motion

Equations

a = v² / r

f = 1/t

v = (2 pi r) / t = 2 pir r f

Fe = (m v²) / r

Fg = GMm / r² (distance between 2 objects not radius)

g = GM / r²

V = root gr

V = root gr tan 0

V = root gMr (different g value)

T = 2 pi root ( r³ / GM ) kelpers 3rd law derived equation for period

Velocity is tangent to the circle

Acceleration is pointing towards the center of the circle (and net force)

Speed is constant but velocity changes due to direction changing

Acceleration is present due to change in velocity

Period - 1 complete revolute / rotation, units is seconds

Frequency - occurrence per time period, units is also seconds

Don’t write Fe write the actual force on FRQs

Only 2 directions in Uniform Constant Motion, Tangent and Center

Tires experience static friction

“Path it takes” → Velocity → Tangent

Dont let direction fool you when making free body diagrams, direction is based on velocity and velocity does not affect free body diagrams

To determine largest tension with different circles, plug radius and mass into force equation and compare the values

Mass isn’t needed to solve velocity (it cancels out when solving) all it depends on is g and r

Radius is inversely proportional to time

Acceleration is inversely proportional with time (kinematics equations)

You need normal force to feel weight, you will feel weightless without normal force

Critical Velocity

add forces like a pulley (causing force is positive, retarding force is negative)

Set normal force to 0

look for words like “Without loosing contact” “Minimum” or “Maximum” speed

at the bottom N force is ALWAYS greater then weight

at the top (inside) W and N force are added

at the highest point normal force can be less then weight (0), more than weight (very fast or small radius) , or equal to weight

Orbital Motion

Closed Trajectory

Experiences free fall → Only force applied is weight → acceleration points towards center of earth

g is only 10 on earth, the moon doesn’t have a g of 10 bc its farther away (farther the distance the weaker g is)

Geostationary orbit - must have same period as the body it is orbiting

When deriving little g the mass of the orbiting object cancels out