AP® Physics 1: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics/units/2/2-4)
Unit 2 · Topic 2.4
2.4 Newton’s First Law
Newton's first law says that when the net force on a system is zero, its velocity doesn't change: it stays at rest or keeps moving in a straight line at constant speed. That balanced condition is called translational equilibrium, and solving equilibrium problems means making the forces add to zero in each direction.
Key terms
- Newton's first law
- inertia
- net force
- translational equilibrium
- inertial reference frame
Net force and the first law
The net force (ΣF) is the vector sum of all forces on a system. Newton's first law says that if ΣF = 0, the velocity is constant. A system at rest stays at rest, and a moving system keeps the same speed and direction.
Inertia is the tendency of an object to keep its velocity. That's why passengers lurch forward when a bus brakes: their bodies keep moving forward until something, like a seatbelt, exerts a force to slow them.
Motion doesn't need a force
The most common misconception in physics is that moving things need a force to keep them going. They don't. A hockey puck on frictionless ice would glide forever. In everyday life things slow down because friction or air resistance acts on them, not because a "force of motion" runs out.
So a crate pushed across a floor at constant velocity has zero net force: your push exactly balances friction. You don't have to push harder than friction to keep it moving at a steady speed, only to speed it up.
Translational equilibrium
A system is in translational equilibrium when ΣF = 0. Because force is a vector, that means ΣF_x = 0 and ΣF_y = 0 separately. Equilibrium includes both "at rest" and "moving at constant velocity."
Solving equilibrium problems: draw a free-body diagram, choose axes, split any angled forces into components and set the sum in each direction to zero. Then solve for the unknowns.
Example: a block sliding down a ramp at constant velocity is in equilibrium. Along the slope, the friction force must exactly cancel the downhill part of gravity, so F_f = mg sin θ. Perpendicular to the slope, F_N = mg cos θ.
Balanced in one direction, not another
Forces can balance along one axis but not the other. A projectile has no horizontal force (balanced, so v_x stays constant) but an unbalanced vertical force (gravity, so v_y changes). Only the velocity component along the unbalanced force changes; the other component stays put.
A sled pulled across level snow at constant speed is balanced in both directions. If the rope is pulled harder, the forces become unbalanced horizontally and the sled speeds up, but the vertical forces can still balance.
Inertial reference frames
An inertial frame is one in which Newton's first law holds: objects with no net force really do keep a constant velocity. Frames moving at constant velocity are inertial. An accelerating car isn't: a ball on the floor rolls backward when the car speeds up, even though no backward force acts on it. Assume inertial frames unless told otherwise.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Hanging sign (classic trap)
A 200 N sign hangs from two cables. Each cable makes a 30° angle with the horizontal, one going up to the left and one up to the right. Find the tension in each cable.
Show the solutionHide the solution
- Step 1: The sign is at rest, so ΣF_x = 0 and ΣF_y = 0.
- Step 2: By symmetry the two tensions are equal; call each T. Horizontally, T cos 30° to the left cancels T cos 30° to the right.
- Step 3: Vertically: 2T sin 30° − 200 N = 0, so T = 200 ÷ (2 × 0.50) = 200 N.
- Step 4: The trap is assuming each cable holds half the weight (100 N). Shallow cables pull mostly sideways, so they need a large tension to supply 100 N each upward. At 10° above horizontal the tension would be about 580 N.
Answer: 200 N in each cable
- Example 2Calculator allowed
Pushing a crate at constant velocity
You push a 25 kg crate across a level floor with a horizontal 80 N force, and it moves at constant velocity. What is the friction force on the crate?
Show the solutionHide the solution
- Step 1: Constant velocity means a = 0, so the net force is zero.
- Step 2: Horizontal forces: your push (80 N forward) and friction (backward). ΣF_x = 80 N − F_f = 0.
- Step 3: F_f = 80 N, pointing opposite the motion. The crate's mass doesn't matter for this question.
Answer: 80 N, opposite the crate's motion
- Example 3Calculator allowed
Evaluating a claim about an elevator
A 1200 kg elevator car rises at a constant 3.0 m/s. A student claims the cable's tension must be greater than the car's weight, because the car is moving up. Evaluate the claim and find the tension. Use g = 9.8 m/s².
Show the solutionHide the solution
- Step 1: Constant velocity means zero acceleration, so by Newton's first law the net force is zero.
- Step 2: Only two forces act: tension up and gravity down. ΣF_y = F_T − mg = 0, so F_T = mg.
- Step 3: F_T = (1200)(9.8) = 11,760 N ≈ 1.2 × 10⁴ N, exactly the car's weight.
- Step 4: The claim is wrong. Tension exceeds the weight only while the car's acceleration points up, such as when it speeds up going up or slows down going down.
Answer: The claim is incorrect; the tension equals the weight, about 1.2 × 10⁴ N
Common mistakes
- Thinking an object moving at constant speed must have a net force in its direction of motion. Constant velocity means zero net force.
- Treating "at rest" as the only kind of equilibrium. Constant velocity is equilibrium too.
- Assuming two cables holding an object each carry half its weight. Only the vertical components share the weight; angled cables carry more.
- Forgetting that equilibrium must hold in both the x and y directions separately.
On the exam
- Expect claims like "the elevator moves upward at constant speed, so the tension is greater than the weight." Respond with the first law: constant velocity means the forces balance, so tension equals weight.
- For equilibrium free-response parts, write ΣF_x = 0 and ΣF_y = 0 with each force's components, then solve. Readers look for the starting principle, not just the final number.
Connected topics
Videos
Check yourself
4 questions on 2.4 Newton’s First Law. Pick an answer to see if you got it, and why.
A worker pushes a crate horizontally with a 50 N force, and the crate slides across the floor at constant velocity. What is the friction force on the crate?
An elevator car is moving upward at constant speed. How does the tension in its cable compare with the car's weight? Ignore air resistance and friction.
A hockey puck slides across ice with negligible friction and air resistance. What is needed to keep it moving at constant velocity?
Which property of an object is the measure of its inertia?
0 of 4 answered