Study notes
Dynamics
The forces that act on objects, the distinction between mass and weight, how a resultant force produces acceleration via F = ma, and how friction and air resistance shape real motion.
Learn it step by step
Contact forces need touching, non-contact forces do not
Contact forces act only where two objects touch: friction (opposes sliding), air resistance (opposes motion through air), tension (pulls through a stretched string or rope), and the normal force (a surface pushing back, perpendicular to itself). Non-contact forces act at a distance with no touching required: gravitational, electrostatic, and magnetic forces.
Mass is constant, weight is a force that depends on location
Mass is the amount of matter in an object, measured in kg, and stays the same everywhere. Weight is the gravitational force pulling on that mass, , where is the gravitational field strength. Since is different on the Moon than on Earth, the same object's mass never changes but its weight does.
Mass is a measure of an object's inertia
Inertia is an object's natural resistance to a change in its motion, whether starting, stopping, speeding up, or changing direction. The greater an object's mass, the greater its inertia, which is why a loaded truck is far harder to get moving or to stop than an empty shopping trolley.
Balanced forces mean no change in motion
When all the forces on an object are balanced (their resultant is zero), the object stays at rest or continues moving at a constant velocity in a straight line. This does not mean no forces are acting, only that they cancel out exactly, so a car cruising at a steady speed still has a driving force balanced by resistive forces.
Unbalanced forces change an object's motion
When the forces on an object do not cancel out, there is a resultant (net) force, and the object's velocity changes, it speeds up, slows down, or changes direction. The bigger the resultant force for a given mass, the bigger that change in velocity per second.
Every force has an equal and opposite reaction force
Forces always occur in pairs: if object A pushes or pulls on object B, then B pushes or pulls back on A with an equal-sized force in the opposite direction. When you push against a wall, the wall pushes back on your hand with the same size of force.
Resultant force equals mass times acceleration
The resultant force acting on an object relates to its mass and acceleration by , where is the resultant force in newtons, is mass in kg, and is acceleration in m/s^2. This is the key equation linking force and motion, and it only ever uses the RESULTANT force, not any single force acting alone.
Friction and air resistance can lead to a terminal velocity
As a falling object speeds up, air resistance acting on it increases. Terminal velocity is reached when air resistance has grown large enough to exactly balance the object's weight, so the resultant force becomes zero and the object then falls at a constant maximum speed rather than continuing to accelerate.
Worked examples
- Use F = ma, rearranged to find acceleration: a = F / m.
- F = 15 N, m = 3 kg.
- a = 15 / 3 = 5 m/s^2.
- The object accelerates at 5 m/s^2 in the direction of the resultant force.
- Use F = ma directly.
- m = 2 kg, a = 4 m/s^2.
- F = 2 x 4 = 8 N.
- The resultant force acting on the object is 8 N.
- Weight uses W = mg, not the mass value alone, mass and weight are different quantities.
- m = 5 kg, g = 10 N/kg.
- W = 5 x 10 = 50 N.
- The rock's weight is 50 N (its mass remains 5 kg, unchanged by location).
- First find the resultant force by combining the two opposing forces: resultant = 20 N (forward) - 8 N (backward, friction) = 12 N forward.
- This is the single resultant force to use in F = ma, not the original 20 N alone.
- a = F / m = 12 / 4 = 3 m/s^2.
- The trolley accelerates at 3 m/s^2 in the forward direction.
Mind map
Mind map for Dynamics.
- Types of force
- contact: friction, air resistance, tension, normal force
- non-contact: gravitational, electrostatic, magnetic
- Mass vs weight
- mass: amount of matter, constant
- weight: W = mg, a force, varies with location
- Inertia
- resistance to change in motion, grows with mass
- Balanced vs unbalanced forces
- balanced: no change in motion
- unbalanced: resultant force changes motion
- Action and reaction
- equal and opposite force pairs
- F = ma
- resultant force = mass x acceleration
- Terminal velocity
- air resistance grows until it balances weight