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Exam prep · AP Physics 1 · Unit guide

AP Physics 1 Unit 2: Force and translational dynamics

Newton's laws, friction, circular motion and gravitation explained

On the exam: Newton’s laws, free-body diagrams, friction, circular motion, gravitation. 18 to 23%.

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AP Physics 1 Unit 2: Force and translational dynamics mindmap: Newton's First Law: Inertia, Newton's Second Law: F equals m a, Newton's Third Law: Action-Reaction, Free-Body Diagrams, Static and Kinetic Friction, Uniform Circular Motion, Newton's Law of Gravitation, Worked Example: Block on an Incline
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Ever think a moving object needs a constant push to keep going? That's the most common mistake in force and motion, and Newton's laws correct it. This is Unit 2 of AP Physics 1, covering Newton's laws, free-body diagrams, friction, circular motion and gravitation, ending with a worked problem.

Newton's First Law: Inertia

Newton's first law says that an object keeps its velocity constant unless a net external force acts on it. That includes staying at rest, but it also includes moving in a straight line at steady speed. On a frictionless surface, a sliding puck needs no push at all to keep moving. The mistake students often make is assuming motion always requires a force; really, only a change in motion does.

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force. Newton's First Law

Key points.

  • Net force zero means no change in velocity
  • Mass resists changes in motion
  • Equilibrium means constant velocity or rest
  • Motion doesn't require a continuous force

Newton's Second Law: F equals m a

Newton's second law ties force, mass and acceleration together: the net force equals mass times acceleration, so acceleration equals net force divided by mass. The unit of force, the newton, is defined as a kilogram meter per second squared. Say the net force on a two kilogram cart is ten newtons; dividing ten by two gives an acceleration of five meters per second squared, in the direction of that net force.

ΣF = m × a
a = ΣF / m
Units: newton = kg·m/s²
Example: ΣF=10N, m=2kg
a = 10/2 = 5 m/s²

Key points.

  • Net force equals mass times acceleration
  • Acceleration equals net force divided by mass
  • Newton is one kilogram meter per second squared
  • Bigger mass needs more force for same acceleration

Newton's Third Law: Action-Reaction

Newton's third law says that when one object pushes on a second, the second pushes back equally hard in the opposite direction, at the same instant. A table pushes up on a book as hard as the book pushes down on the table. These two forces never cancel, since they act on different objects. What matters for one object's acceleration is only the forces acting on that object, not its own reaction pair.

Action-Reaction Pairs

  • Equal magnitude, opposite direction
  • Act on two different objects
  • Same type of force
  • Occur at the same instant

Net Force on One Object

  • Sum of all forces on that object
  • Can include many different force pairs
  • Determines that object's acceleration
  • Never includes its own reaction force

Free-Body Diagrams

A free-body diagram isolates one object and shows every force acting on it as an arrow, with length suggesting size and direction showing where it points. For a block on a ramp, you'd draw weight pointing straight down, the normal force perpendicular to the ramp's surface, and friction along the surface opposing sliding. Tilting your axes to match the incline makes it easier to apply Newton's second law separately along and perpendicular to the slope.

Key points.

  • Isolate one object and draw every force on it
  • Arrows show direction and relative size
  • Tilt axes to match an incline
  • Use the diagram to apply Newton's second law

Static and Kinetic Friction

Friction resists relative sliding between two surfaces. Static friction can take any value up to a maximum equal to the coefficient of static friction times the normal force, adjusting itself to prevent motion. Once an object slides, kinetic friction takes over, equal to the coefficient of kinetic friction times the normal force, usually a bit smaller. That's why it takes more force to start sliding a crate than to keep it sliding.

fs ≤ μs × N (max static)
fk = μk × N (kinetic)
μs is usually > μk
Friction opposes relative sliding

Key points.

  • Static friction adjusts up to a maximum value
  • Kinetic friction is roughly constant while sliding
  • Static coefficient usually exceeds kinetic coefficient
  • Friction always opposes relative sliding motion

Uniform Circular Motion

An object moving at constant speed in a circle still accelerates, because its direction keeps changing; that's centripetal acceleration, equal to velocity squared over radius, always pointing toward the center. The net force producing it isn't a new kind of force; it's whatever combination of gravity, tension, friction or normal force points inward. For a car at four meters per second on a two meter radius curve, that acceleration is eight meters per second squared.

ac = v² / r
ΣFc = m v² / r
Points toward the center
v = 4 m/s, r = 2 m
ac = 16/2 = 8 m/s²

Key points.

  • Centripetal acceleration points toward the circle's center
  • Equals velocity squared divided by radius
  • Centripetal force is just the net inward force
  • Can come from tension, gravity, friction or normal force

Newton's Law of Gravitation

Newton's law of gravitation says every pair of masses attracts with a force equal to a constant, G, times the product of the masses, divided by the distance between their centers squared. Near Earth's surface, that formula simplifies to the familiar g, about nine point eight meters per second squared, found by plugging Earth's mass and radius into the equation. Move twice as far from Earth's center, and gravitational force drops to one quarter of its original value.

Fg = G m1 m2 / r²
G ≈ 6.67×10⁻¹¹ N·m²/kg²
g = G M / r²
g ≈ 9.8 m/s² at surface

Key points.

  • Gravitational force depends on both masses
  • Force falls off with distance squared
  • Surface gravity comes from Earth's mass and radius
  • Doubling distance cuts force to one quarter

Worked Example: Block on an Incline

Picture a five kilogram block sliding down a thirty degree ramp with a kinetic friction coefficient of zero point two. Weight's component along the slope is about twenty four point five newtons, and the component into the surface gives a normal force near forty two point four newtons, making friction about eight point five newtons. Dividing the net force by mass gives an acceleration of roughly three point two meters per second squared down the ramp.

  1. Draw the free-body diagram: weight, normal, friction
  2. Resolve weight into components along and perpendicular to the ramp
  3. Use the perpendicular direction to find the normal force
  4. Apply Newton's second law along the ramp
  5. Solve for acceleration using the given numbers

Remember this

The one thing to remember: forces change motion, they don't maintain it, and every problem starts with a clean free-body diagram. Now quiz yourself on this AP Physics 1 material to see what really sticks.

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