Push a book across a table and it slides to a stop — so it feels obvious that things need a force to keep moving. Newton saw deeper. His first law says the opposite: an object only changes its motion when a resultant force acts on it. Left alone, it keeps doing exactly what it was doing — sitting still, or gliding at a steady speed forever. The book stops only because friction is quietly pushing back.
📘 What you need to know
Newton’s laws link the forces on an object to its motion
First law: a body stays at rest or moves with constant velocity unless acted on by a resultant force
So a resultant force is what changes motion — speeding up, slowing down, or changing direction
If the resultant force is zero, the object is in translational equilibrium
An object in equilibrium is either at rest or moving at constant velocity — both count
Constant velocity does not mean no forces — it means the forces are balanced
What the law actually says
Here’s the statement in full:
Newton’s First Law
A body remains at rest or moves with constant velocity unless acted on by a resultant force
Read it as two promises. First: an object at rest stays at rest until something pushes it. Second: an object already moving keeps moving at the same speed in the same straight line — the same constant velocity — until something pushes it. In both cases, the “something” is a resultant force: the single leftover force once you’ve added up everything acting on the object.
Turn that around and you get the useful version. If an object’s motion isn’t changing, the resultant force on it must be zero. The forces are all there — they just cancel out.
Both footballs obey the first law: the up and down forces balance, so the resultant force is zero. One stays still; the other keeps gliding at a steady speed. Zero resultant force covers both.
This is the bit that trips everyone up. “No resultant force” doesn’t mean “not moving” — it means “not changing how it moves.” A spacecraft coasting through deep space has essentially no forces on it and never slows down. On Earth, friction and drag are the hidden forces that make constant motion look like it needs a constant push. Remove them and things just keep going.
Resultant force changes motion
So what does a resultant force actually do? It changes an object’s motion in one of three ways:
speeds up
or
slows down
or
changes direction
Any one of these counts as a change in velocity — and velocity is a vector, so even changing direction at a steady speed needs a resultant force. If none of these three things is happening, you can say with confidence: the resultant force is zero.
Translational equilibrium
When the resultant force on an object is zero, the object is said to be in translational equilibrium. It’s just a formal name for “balanced forces,” and it’s the condition behind every “constant velocity” or “at rest” problem you’ll meet.
Translational equilibrium
resultant force = 0 → object is at rest OR moving at constant velocity
Because force is a vector, “balanced” has to hold in every direction at once. In practice you split the forces into horizontal and vertical components and check each:
🛠️ Checking for equilibrium
Split the forces into horizontal and vertical components.
Add the horizontal forces: the total pushing left must equal the total pushing right.
Add the vertical forces: the total pushing up must equal the total pushing down.
If both balance, the resultant is zero — the object is in equilibrium (at rest or constant velocity).
WE 1
A car travels along a level road at a constant velocity. Its engine provides a driving force of 4200 N pushing it forward. Assuming the only horizontal force opposing the car is the total resistance (friction and air drag), find the size of that resistive force.
At constant velocity the driving force and the resistance are drawn the same length — they must be equal.
Step 1 — what does constant velocity tell us?
constant velocity → no change in motion
→ resultant force = 0 (equilibrium)
Step 2 — balance the horizontal forces
driving force = resistive force
resistance = 4200 Nresistive force = 4200 N (4.2 kN)The car keeps a steady speed not because there’s no force, but because the forward and backward forces exactly cancel.
WE 2
A lamp of mass 2.5 kg hangs motionless from a single cable. Taking g = 9.81 m s−2, find the tension in the cable.
Step 1 — the lamp is at rest, so it’s in equilibrium
resultant force = 0
→ tension up = weight down
Step 2 — find the weightFg = mg = 2.5 × 9.81 = 24.5 NStep 3 — the tension balances ittension = 24.5 N upwardNo motion means the two vertical forces must be equal — so the tension simply matches the weight.
💡 Top tips
Constant velocity = balanced forces. Whenever a question says “constant speed,” “steady velocity,” or “moves at a constant rate,” write “resultant force = 0” straight away.
Equilibrium works direction by direction. Check horizontal and vertical separately — both must balance.
“At rest” and “constant velocity” are the same case as far as the first law is concerned: both mean zero resultant force.
The word is resultant. The law is about the leftover force after adding everything up, not the individual forces — those can be huge and still cancel.
WE 3
A crate has four forces on it: 18 N left, 18 N right, 25 N up, and 25 N down. Is the crate in equilibrium, and what can you say about its motion?
Step 1 — add the horizontal forces18 right − 18 left = 0 NStep 2 — add the vertical forces25 up − 25 down = 0 NStep 3 — both directions balance
resultant force = 0 → in equilibrium
yes — equilibriumBy the first law it’s either at rest or moving at constant velocity — the forces alone can’t tell you which; you’d need to know how it was already moving.
Quick recap: a resultant force is the only thing that changes motion. Zero resultant force means the object is in translational equilibrium — at rest or at constant velocity. Constant velocity never means “no forces”; it means the forces balance in every direction.
⚠ Common mistakes
Thinking a moving object needs a constant force to keep moving — it only needs one to change its motion
Assuming constant velocity means no forces act — it means the forces are balanced
Forgetting that changing direction at steady speed still needs a resultant force (velocity is a vector)
Checking only one direction — equilibrium needs the forces to balance horizontally and vertically
Treating “at rest” and “constant velocity” as different physics — both are simply zero resultant force
The first law tells us when motion changes — only when there’s a resultant force. But it doesn’t say by how much. For that we need the next piece: Newton’s Second Law, which links the size of the resultant force to the acceleration it produces through F = ma.
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