AP Physics 1 Unit 3 Cheat Sheet: Circular Motion and Gravitation

AP Physics 1 Unit 3: Circular Motion and Gravitation

TLDR

• Circular motion requires a constant inward net force.

• Speed can stay constant while velocity changes direction.

• Centripetal force is the result of real forces, not a new force.

• Gravity explains falling objects, satellites, and planetary orbits.

• Many AP questions combine circular motion with force analysis.

Why This Unit Matters

Unit 3 pushes students from straight line motion into curved motion and long range forces. This is where many students first struggle conceptually, because motion and force are no longer aligned in the same direction.

On the AP Physics 1 exam, this unit tests whether you truly understand vectors, force direction, and cause versus effect. Circular motion and gravitation also appear later in energy and momentum problems, making this a critical bridge unit.

1. Uniform Circular Motion

Uniform circular motion describes motion at a constant speed along a circular path.

Key ideas:

• Speed is constant.

• Velocity is not constant because direction changes.

• A changing velocity means acceleration exists.

Even when an object moves at steady speed, it is accelerating if it moves in a circle.

2. Centripetal Acceleration

Centripetal acceleration always points toward the center of the circle.

Key relationship:
aᶜ = v² ÷ r

Important observations:

• Acceleration is perpendicular to velocity.

• Larger speed increases centripetal acceleration.

• Smaller radius increases centripetal acceleration.

This inward acceleration is what keeps the object moving in a curved path.

3. Centripetal Force

Centripetal force is the net inward force that causes circular motion.

Key relationship:
Fᶜ = mv² ÷ r

Critical clarification:

• Centripetal force is not a new type of force.

• It is provided by real forces such as tension, friction, normal force, or gravity.

You must identify which actual force or combination of forces points inward.

Tutor Tip
Never draw “centripetal force” as its own arrow on a free body diagram. Always draw the real forces and show that their net points toward the center.

4. Tangential Motion and Broken Circles

Velocity in circular motion is always tangent to the circle.

If the inward force suddenly disappears:

• The object does not fly outward.

• It moves in a straight line tangent to the circle.

This concept is tested frequently using diagrams and explanation questions.

5. Gravitational Force

Gravity is a universal force acting between all masses.

Key equation:
Fᵍ = Gm₁m₂ ÷ r²

Important points:

• Gravity is always attractive.

• Distance is measured from center to center.

• Increasing distance rapidly decreases force.

This same force explains falling objects and orbital motion.

6. Orbits and Circular Motion

Orbits occur when gravity provides the centripetal force.

In orbital motion:

• Gravitational force points toward the center of the orbit.

• This force causes continuous centripetal acceleration.

• Satellites are constantly falling but missing the surface.

Orbital speed depends on distance from the central body, not mass of the satellite.

7. Gravitational Acceleration Near Earth

Near Earth’s surface:
g = GM ÷ r²

This explains why:

• Gravitational acceleration is nearly constant near Earth.

• Objects of different mass fall at the same rate.

• Weight depends on location, not just mass.

This relationship is often tested conceptually rather than numerically.

Common Pitfalls

• Thinking centripetal force is a separate force

• Drawing centripetal force in free body diagrams

• Confusing tangential and radial directions

• Using diameter instead of radius

• Measuring gravitational distance incorrectly

• Assuming heavier objects fall faster

• Forgetting that velocity direction is constantly changing

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