Laws of Motion lessons
Why things move
A cart on a track: hold Push, set the force and mass, and watch a = F / m draw the velocity-time graph.
A push or a pull is called a force. Forces make things start, stop, speed up, slow down or turn.
In the cart above, a bigger push gives a bigger acceleration. A heavier cart speeds up more slowly with the same push.
Isaac Newton described these links in his three laws of motion. In this course you will use them to predict how things move.
Velocity and acceleration
Speed is how fast something moves, in metres per second (m/s). Velocity is speed in a given direction, like 12 m/s to the right.
Acceleration is how fast the velocity changes. It is the change in velocity, \Delta v, divided by the time taken.
Acceleration: a = \frac{\Delta v}{t}
On a velocity-time graph, the slope of the line is the acceleration. The area under the line is the distance travelled.
A velocity-time graph in three phases: each phase shows its slope as the acceleration and its shaded area as the distance.
Practice: Read a velocity-time graph
Read an acceleration (slope) or a distance (area) off a random velocity-time graph.
Forces and free-body diagrams
Forces are measured in newtons (N). Every force has a size and a direction, so we draw it as an arrow.
A free-body diagram shows one object and every force acting on it. A longer arrow means a bigger force.
Common forces are weight (gravity pulling down), the normal force (a surface pushing back), friction and tension in a rope or cable.
Free-body diagrams for a hanging lamp, a pushed crate, a falling skydiver and a car, with arrows drawn to scale.
Practice: Label the forces
Drag force names onto the arrows of a free-body diagram.
Resultant force
The resultant force is the one force that has the same effect as all the forces together. Add forces that point the same way and subtract forces that point opposite ways.
If the resultant is zero, the forces are balanced. If not, they are unbalanced and the object accelerates in the direction of the resultant.
Two forces pull a crate either way; the resultant arrow shows their difference and says whether the crate accelerates.
Practice: Find the resultant force
Type the size of the resultant force on a crate and pick its direction.
Newton's first law
Newton's first law says an object stays still, or keeps moving at a steady velocity, unless a resultant force acts on it.
Sliding things seem to stop by themselves, but friction is the force stopping them. With no friction at all, a sliding object would never stop.
An object's tendency to keep doing what it is doing is called inertia. More mass means more inertia.
Four pucks slide off at 4 m/s on carpet, wood, ice and a frictionless surface; less friction means a longer slide.
Newton's second law
Newton's second law links the resultant force on an object to its acceleration. More force gives more acceleration, and more mass gives less.
Newton's second law: F = ma
Here F is the resultant force in newtons, m is the mass in kilograms and a is the acceleration in \text{m/s}^2. You can rearrange it to a = \frac{F}{m} or m = \frac{F}{a}.
Three worked F = ma problems: find the acceleration of a car, the force on a trolley and the mass of a cyclist.
Practice: Use F = ma
Find the force, mass or acceleration in a random F = ma problem.
Weight and mass
Mass is the amount of matter in an object, measured in kilograms. It is the same everywhere.
Weight is the force of gravity on that mass, measured in newtons. It depends on the gravitational field strength g, which is 9.8\ \text{N/kg} on Earth.
Weight: W = mg
On the Moon, g is only 1.6\ \text{N/kg}, so you would weigh about a sixth as much. Your mass would not change at all.
The same mass hangs from a spring scale on Earth, the Moon, Mars and Jupiter; its weight changes with g.
Practice: Mass or weight?
Sort facts into mass or weight.
Friction and air resistance
Friction acts where surfaces slide, or try to slide, over each other. It always points against the motion.
Air resistance is friction from the air, and it grows as you go faster. A falling skydiver speeds up until air resistance matches their weight.
Then the forces are balanced, so the speed stops changing. This top speed is called the terminal velocity.
A skydiver falls: air resistance grows with speed until it matches weight, then the parachute opens and a slower terminal velocity is reached.
Practice: Read the skydive
Pick the free-body diagram that matches each stage of a skydive.
Newton's third law
Newton's third law says that when object A pushes or pulls on object B, B pushes or pulls back on A. The two forces are equal in size and opposite in direction.
The two forces always act on different objects, and they are the same type of force. That is why they never cancel each other out.
Force pairs for walking, a rocket, an apple and Earth, and a swimmer pushing off a wall.
Practice: Find the partner force
Match each force to its third-law partner.
Momentum and collisions
Momentum is mass multiplied by velocity. It tells you how hard a moving object is to stop.
Momentum: p = mv
Momentum is measured in \text{kg m/s} and has a direction. When objects collide with no outside force, the total momentum before equals the total momentum after.
This is the conservation of momentum. It works for crashes, explosions and objects that stick together.
Trolley A hits trolley B and they stick; momentum bars show the total stays the same before and after.
Practice: Collisions
Use conservation of momentum to find a velocity after two trolleys collide.
Impulse
A force acting for a time changes an object's momentum. Force multiplied by time is called impulse.
Impulse: Ft = \Delta p
For the same change in momentum, a longer stopping time means a smaller force. Airbags, crumple zones and crash mats all work this way.
A force-time graph for stopping a passenger: the area stays the same, so a longer stop means a smaller force.
Practice: Impulse
Find a force, time or change in momentum using Ft = Δp.
Equations of motion
When the acceleration is constant, five quantities describe the motion. They are the displacement s, starting velocity u, final velocity v, acceleration a and time t.
v = u + at(no s)s = ut + \frac{1}{2}at^2(no v)v^2 = u^2 + 2as(no t)
Each equation leaves out one quantity. Pick the one that holds the three values you know and the one you want.
Three worked problems: list what you know, pick the equation without the missing quantity, then solve.
Practice: Pick the equation
Choose the equation of motion that solves each problem.
Projectile motion
A projectile is anything launched that then moves under gravity alone. Its path is a curve called a parabola.
The sideways and downward motions are independent. Sideways the velocity stays the same, while downwards it grows by 9.8 m/s every second.
So a ball fired sideways lands at the same moment as a ball dropped from the same height. The time to fall is t = \sqrt{\frac{2h}{g}}.
A ball fired sideways off a cliff next to a ball that is dropped: equal sideways steps, growing downward steps, and they land together.
Practice: Projectile problems
Find the flight time or the landing distance of a ball fired sideways off a cliff.
Practice: Which law?
Sort everyday events by the law of motion that explains them.