This document provides an overview of key physics concepts related to gravitation and circular motion. It defines important terms like vector, force, centripetal force, and gravitational field. It lists important formulas used to calculate velocity, centripetal acceleration, gravitational force, and more. It also describes units of measurement and provides an example problem calculating gravitational attraction between two boulders.

1. AP Physics - Core Concept Cheat Sheet
09: Gravitation and Circular Motion
Key Physics Terms
• Vector: A quantity that represents magnitude (size) and
direction. It is usually represented with an arrow to indicate
the direction; arrow may be drawn to scale.
• Vector Component: The perpendicular parts into which a
vector can be separated and that act in different directions
from the vector.
• Resultant: The result of adding two or more vectors;
vector sum.
• Vector Addition: The process of combining vectors;
added tip to tail.
• Force: A vector quantity that tends to accelerate an
object; a push or a pull.
• Centripetal Force: A center seeking force for an object
moving in a circular path.
• Centrifugal Force: An apparent, outward pointing force
for an object moving in a circular path. A rotating object
may seem to be pushed outward, but actually must be
pulled inward in order to maintain any circular path.
• Inverse Square Law: A relationship relating the strength
of an effect to the inverse square of the distance away
from the source.
• Gravitational Field: The map of influence that a massive
body extends into space around itself.
• Linear Speed: Straight path distance moved per unit of
time, also referred to as tangential speed.
• Velocity: The distance an object travels per unit of time
including its direction of motion.
• Rotational Speed: Number of rotations or revolutions per
unit of time, often revolutions per minute, rpm.
• Normal Force: Support force that acts perpendicular to a
surface. If the surface is horizontal, this force balances the
weight of the object. If the surface is banked, the normal
force is a reaction force, still perpendicular to the surface,
to a component of the weight.
• Universal Gravitational Constant: A proportionality
constant that relates the strength of gravitational attraction
in Newton’s law of universal gravitation.
Variables Used
• v = velocity (usually average velocity or constant velocity)
• ac = centripetal acceleration
• Fg = force from gravity
• Fc = centripetal force
• Δ = change in
• θ = angle
• m = mass
• d = distance
Key Formulas
• Pythagorean Theorem: c2 = a2 + b2
• Sin θ = opp / hyp
• Cos θ = adj / hyp
• Tan θ = opp / adj
• Fnet = ma
• Fg = Gm1m2 / d2
• G=6.67 x 10-11 Nm2/ kg2
• ac = v2 / r
• Fc = mv2 / r
Key Metric Units
• Velocity: m/s
• Linear speed: m/s
• Rotational speed: revolutions per unit of time
• Distance: meters, m
• Time: seconds, s
• Acceleration (linear or centripetal): m/s2
• Force (gravitational, centripetal, etc): Newton, N
• Mass: kilograms, kg
Weightlessness
• Weightlessness: Astronauts “floating” in space may appear
to be weightless. However, the pull from gravity definitely
still acts on them. If it didn’t, their inertia would carry them
off in a straight line never to return to the earth. Instead,
the pull from gravity acts as a centripetal force to maintain
their orbit about the earth.
Centripetal Force Diagram
• The object is moving in a circular path and it depicted at
various points along that path.
• Note how the centripetal force always points towards the
center of the circle.
• Note how the linear speed at any given instant always points
tangent to the circular path.
Instantaneous
velocity
Centripetal
force
Gravitation and Circular Motion Problem
Solving Tips
• These tips will make it easier to solve any physics problems.
• Thoroughly read the entire problem.
• Draw a diagram if needed. Identify all given information. Be
sure to make diagrams or calculations with direction in
mind.
• Identify the quantity to be found.
• Select appropriate formula(s) that incorporate what you
know and what you want to find.
• Convert units if needed. Use units throughout your
calculations.
• Do any mathematical calculations carefully.
Typical Gravitational Problem
Example: Calculate the gravitational attraction between two
10,000 kg boulders whose centers sit 20 m apart.
Known: Each mass = 10,000 kg Distance = 20 m
Unknown: Gravitational attraction, Fg
Define: Fg = Gm1m2 / d2
Also needed: G = 6.67x10-11 Nm2 / kg2
Output:
-11 2 2
(6.67 x 10 Nm F / kg )(10,000 kg)(10,000 kg)
g 2
gF = 1.7 x 10− N
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(20 m)
=
5
Substantiate: Units are correct, sig fig correct, magnitude is
reasonable.
Note how all the units would cancel except the Newton label.
Note the small attraction of gravity. This is due to the
relatively small masses. Solar or planetary scale objects
would posses much greater gravitational pulls.
How to Use This Cheat Sheet: These are the keys related this topic. Try to read through it carefully twice then write it out on a
blank sheet of paper. Review it again before the exams.