Physics Circular Motion Review

Centripetal Force

F_c → Sum of the forces causing an object to move in a circle

• F_c= mv²/ r

Centripetal Acceleration

A_c → ALWAYS towards the center of the circle (causes things to move in a circle)

• A_c= v²/r

Velocity for circular motion

Circumference divided by the period (time it takes to complete one revolution)

• V= 2(π)(r)/ T

Law of universal gravitation 

F_g= GmM / r²

• G= 6.67×10^-11

Relationship between mass and Force of Gravity 

Direct linear relationship 

• whatever happens to mass (m and M) will happen to gravity 

• ex. if m is doubled then F_g will also double

Relationship between Radius and Force of gravity

inverse square root

• whatever happens to the radius distance flip it then square it and that will be what happens to F_g

• ex. if I ½ the radius distance than F_g will be 4 times bigger

Normal Force= 0

Item is no longer in contact with the surface

• when question asks about minimum speed for something to not fall → set F_N to 0

What direction is centripetal acceleration

Always towards the center of the circle!

• things must be accelerating to go in a circle (one force must be greater than another)

What direction is velocity 

tangent to the circle!

• velocity is not constant because it is a vector and the direction is always changing 

When and why do we feel weightless

At the top of a hill because we feel normal force

• at the top of a hill you are accelerating down (toward the center) which means mg is bigger than F_N 

When and why do we feel heavier

at the bottom of hills because normal force is greater 

• at the top of the hill you are accelerating up (toward the center) which means F_N is bigger than mg

How to find Centripetal Force Equation

F_c= forces toward the center - forces away from the center

substitution for friction

coefficient of friction times normal force

Circular motion with two masses

make free body diagrams and net force equations for both and then try to combine them (usually cancelling out a tension force)

• ex. item on the table and washer hanging through a hole

• REMEMBER to label the masses as m₁ and m₂

Acceleration and Force constant?

NOOOO! Acceleration and force are vectors so they are never constant

uniform circular motion

circle at constant speed

weightless/ 0 normal force equation to find velocity

v= sqrt. rg

Forces have…

equal and opposite reactions

Solving relationship of variables questions

• use one for everything and see what happens!

• look at what is the same and cancel it out! just look at what is changing

Traditional net force equation

force= mass x acceleration

(still applies for circular motion)

Sign of forces TOWARDS the center of a circle

POSITIVE

Sign of forces AWAY from the center of the circle 

NEGATIVE 

Force of Gravity problems

Be sure to include the radius from the center if things are on the outside surface of the planet