AP Physics 1 forces and Newton's laws
Unit 2 of AP Physics 1 is about forces and how they change motion. Almost every later unit builds on it.
On this page
- Newton's three laws
- Free-body diagrams
- The forces you meet most
- Slopes
- Circular motion and gravitation
- Common mistakes
- Worked examples
- Practice questions
- Frequently asked questions
- The key ideas in more depth
- More practice
- One more worked example
- Extra practice
- More questions students ask
- Key takeaways
- Quick check
Newton's three laws
- First law: an object keeps its velocity unless a net force acts on it. Zero net force means constant velocity, not necessarily rest.
- Second law: ΣF = ma. The net force sets the acceleration.
- Third law: forces come in pairs that are equal in size, opposite in direction and act on different objects.
Free-body diagrams
Draw the object as a dot and show every force acting on it, and only those forces. Label each one, such as Fg, FN, Ff or FT. There is no "force of motion".
The forces you meet most
- Weight Fg = mg, toward the centre of the Earth.
- Normal force, perpendicular to a surface. It is not always equal to mg.
- Friction: static friction up to μsFN, kinetic friction equal to μkFN.
- Tension in ropes and strings, pulling along the string.
- Spring force F = −kΔx.
Slopes
On an incline, split weight into components: mg sinθ along the slope and mg cosθ into it. Choose axes along and perpendicular to the slope.
Circular motion and gravitation
- Moving in a circle at constant speed still means accelerating, toward the centre: ac = v²/r.
- The centripetal force is not a new force. It is the net inward force from gravity, tension, friction or a normal force.
- Gravity between masses follows F = Gm1m2/r².
Common mistakes
- Drawing a "centripetal force" as an extra arrow on a free-body diagram.
- Assuming the normal force always equals mg.
- Applying Newton's third law to two forces on the same object.
Worked examples
Example 1: two blocks connected
A 3 kg block on a frictionless table is connected over a pulley to a 2 kg hanging block. Find the acceleration. Use g = 9.8 m/s².
- Treat both blocks as one system: the net force is the hanging weight, 2 × 9.8 = 19.6 N.
- a = 19.6/(3 + 2) = 3.92 m/s².
- Tension, from the 3 kg block: T = 3 × 3.92 ≈ 11.8 N, less than the hanging weight, as it must be.
Example 2: an elevator
A 60 kg person stands on a scale in an elevator accelerating upward at 2 m/s². What does the scale read?
- FN − mg = ma, so FN = 60(9.8 + 2) = 708 N. The scale reads more than the person's weight (588 N).
Example 3: friction on a flat surface
A 5 kg box rests on a floor with μs = 0.4. What horizontal force starts it moving?
- Maximum static friction = 0.4 × 5 × 9.8 = 19.6 N. A push just over this starts it moving.
Example 4: a car on a curve
What is the maximum speed for a car on a flat curve of radius 40 m if μs = 0.6?
- Friction provides the centripetal force: μmg = mv²/r, so v = √(μgr) = √(0.6 × 9.8 × 40) ≈ 15.3 m/s. The mass cancels.
Practice questions
Try each one before opening the answer.
Q1. A 10 kg crate is pulled across a floor by a 50 N horizontal force. μk = 0.3. Find the acceleration.
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Q2. A book rests on a table. Name the Newton's third law pair of the book's weight.
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Q3. At the top of a loop, a roller coaster car is upside down. Which forces provide the centripetal force?
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Frequently asked questions
Is the normal force always equal to mg?
No. It equals mg only on a flat surface with no other vertical forces and no vertical acceleration. On slopes it is mg cosθ; in a lift it changes with acceleration.
What is the difference between mass and weight?
Mass (kg) is the amount of matter and does not change. Weight (N) is the gravitational force mg and depends on g.
The key ideas in more depth
Every force problem follows the same pattern: identify the object, draw every force on it, choose axes, write ΣF = ma for each axis, and solve. Most mistakes come from the diagram, not the algebra. Spend your effort there.
Choose axes that make the maths easy. On a slope, use axes along and perpendicular to the surface. In circular motion, point one axis toward the centre of the circle, because that is the direction of the acceleration.
More practice
Try each one before opening the answer.
Q1. A 50 kg person stands in an elevator moving down at constant speed. What does the scale read?
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One more worked example
Example 5: a rope at an angle
A 20 kg sled is pulled along flat, frictionless ice by a rope at 30° above the horizontal with a tension of 60 N. Find the acceleration and the normal force.
- Horizontal: 60 cos30° ≈ 52 N, so a = 52/20 ≈ 2.6 m/s².
- Vertical: FN + 60 sin30° = 20 × 9.8, so FN = 196 − 30 = 166 N, less than the weight because the rope pulls partly upward.
Extra practice
Try each one before opening the answer.
Q1. A 5 kg box hangs from two ropes, each at 45° to the vertical. Find the tension in each rope.
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More questions students ask
Why is friction sometimes in the direction of motion?
Friction opposes slipping between surfaces, not motion itself. When you walk, friction on your shoe points forward and pushes you along.
Key takeaways
- Draw a free-body diagram before every force calculation.
- Newton's second law uses the net force: ΣF = ma.
- Third law pairs act on different objects.
- The normal force is not always mg.
- Centripetal force is the net inward force, not an extra force.
Quick check
Can an object be moving if the net force on it is zero?