Planes and axes of movement
To describe any movement, we use three imaginary flat sheets called planes. Each plane has an axis, a line the body turns around. The axis is always at right angles to its plane.
- Sagittal plane (splits left and right) with the frontal (transverse) axis: flexion and extension. Examples: running, kicking a ball, a somersault, a bicep curl.
- Frontal plane (splits front and back) with the sagittal axis: abduction and adduction. Examples: star jump, cartwheel, side step.
- Transverse plane (splits top and bottom) with the longitudinal (vertical) axis: rotation. Examples: discus throw, a full twist in a jump, a golf swing.
Tip: imagine a stick through the joint. The joint turns around the stick (axis) and moves within the sheet (plane).
Levers in the body
A lever is a rigid bar that turns on a pivot. In the body, bones are the bars, joints are the pivots (fulcrum), muscles give the effort and the body weight or an object is the load.
- First class (fulcrum in the middle): nodding the head, the neck joint between face weight and neck muscles. Also elbow extension by the triceps.
- Second class (load in the middle): rising on tiptoe; the ball of the foot is the pivot, body weight is in the middle, calf muscle pulls at the heel.
- Third class (effort in the middle): bicep curl, kicking with the knee. Most body levers are this type.
Mechanical advantage
Mechanical advantage = effort arm ÷ load arm. The effort arm is the distance from pivot to effort; the load arm is from pivot to load. Second-class levers have MA > 1: they lift heavy loads with less force. Third-class levers have MA < 1: they need more force but move the load fast and far, which is great for throwing and striking. A bat or racket makes the load arm even longer, so the end moves even faster.
Newton's laws, friction and stability
- First law (inertia): a body stays still or keeps moving at the same speed in a straight line unless a force acts. A ball on the penalty spot stays put until kicked.
- Second law (acceleration): F = m × a. A bigger force gives a bigger acceleration; a heavier body needs more force. Also, impulse = force × time = change in momentum. Bending the knees when landing makes the time longer, so the force is smaller.
- Third law (action and reaction): every force has an equal and opposite force. A sprinter pushes back on the blocks; the ground reaction force pushes the sprinter forward.
Friction
Friction is a force that opposes sliding. Spikes, studs and rubber soles increase friction for grip. Ice skates and smooth skis reduce it. Rough surfaces and a bigger push between surfaces give more friction.
Centre of gravity, balance and equilibrium
The centre of gravity (CoG) is the point where the whole body weight seems to act. A body is stable when its line of gravity (a line straight down from the CoG) falls inside the base of support. More stable = low CoG, wide base, line of gravity near the middle, more mass. Static equilibrium: balanced and still (a handstand). Dynamic equilibrium: balanced while moving at steady velocity (a cyclist at constant speed). A sprinter in the "set" position deliberately moves the CoG in front of the hands to fall forward into the start.
Linear and angular motion
Linear motion: the whole body moves the same distance in the same direction (a sprinter, a sledge). Key ideas: distance, displacement, speed = distance ÷ time, velocity, acceleration, and momentum = mass × velocity.
Angular motion: turning around an axis (a gymnast on a bar). It needs a torque (a force that does not pass through the axis): torque = force × perpendicular distance.
- Moment of inertia (I): how hard it is to change the spin. Mass far from the axis = big I. Tucking makes I small.
- Angular velocity (ω): how fast it turns (rad/s or turns per second).
- Angular momentum L = I × ω. In the air there is no outside torque, so L stays the same: tuck (smaller I) → faster spin; open out (bigger I) → slower spin.
General motion mixes both: a cyclist moves forward (linear) while the legs and wheels turn (angular).
Projectile motion
A projectile is any object or body moving through the air with only gravity (and air resistance) acting: a shot put, a long jumper, a football. Without air, the path is a smooth curve called a parabola.
Three release factors decide the distance:
- Speed of release: the biggest factor. Double the speed and (without air) the range becomes about four times.
- Angle of release: from ground level the best angle is 45°. If you release above the landing level (shot put from about 2 m), the best angle is a little less, around 40°. Long jumpers take off at about 20°–25° because they cannot keep their speed at a steep angle.
- Height of release: a higher release gives more flight time and more distance; tall throwers have an advantage.
Useful equations with no air resistance (from ground level): time of flight t = 2u sinθ ÷ g, range R = u² sin2θ ÷ g, maximum height H = u² sin²θ ÷ 2g, with g = 9.81 m/s².
Heavy objects (shot) follow a nearly perfect parabola. Light ones (shuttlecock) are pulled off the parabola by air: they fall steeply at the end.
Fluid mechanics: drag, lift and spin
Air and water are fluids. Moving through them causes drag, a force that pushes back against the motion. Drag grows with speed (roughly with speed squared), the frontal area facing the flow, the shape and the surface. Cyclists crouch low, swimmers stretch out and wear smooth suits, and helmets are streamlined.
Lift and Bernoulli
When air flows faster over one side of an object, the pressure on that side is lower (Bernoulli's principle). The pressure difference creates lift. A discus or javelin held at a small angle of attack gets lift and flies further. A racing car's spoiler is an upside-down wing that pushes it down for grip.
Spin: the Magnus effect
A spinning ball drags air round with it. On one side the air moves faster, so pressure is lower there and the ball curves towards that side. Topspin makes a tennis ball dip; backspin makes a golf ball float longer; sidespin bends a free kick around a wall.
Key formulas and definitions
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Worked examples
1. Name the plane and axis for (a) a forward roll, (b) a cartwheel, (c) a full twist in a high jump.
(a) Sagittal plane, frontal (transverse) axis. (b) Frontal plane, sagittal axis. (c) Transverse plane, longitudinal axis.
2. In a bicep curl the biceps attaches 4 cm from the elbow and the dumbbell is 32 cm from the elbow. Find the mechanical advantage and say what it means.
MA = effort arm ÷ load arm = 4 ÷ 32 = 0.125. It is less than 1, so the muscle must pull 8 times harder than the dumbbell's weight, but the hand moves 8 times further and faster than the muscle shortens.
3. A 60 kg sprinter pushes off with a net forward force of 480 N. What is her acceleration?
a = F ÷ m = 480 ÷ 60 = 8 m/s².
4. A 0.45 kg football is kicked from rest to 20 m/s. The foot touches the ball for 0.01 s. Find the change in momentum and the average force.
Δp = m × v = 0.45 × 20 = 9 kg m/s. Impulse = F × t, so F = 9 ÷ 0.01 = 900 N.
5. A diver leaves the board with I = 12 kg m² spinning at 2 rad/s. She tucks to I = 4 kg m². Find her new spin rate.
L = I × ω = 12 × 2 = 24 kg m²/s stays the same. New ω = 24 ÷ 4 = 6 rad/s, three times faster.
6. A ball is kicked from the ground at 15 m/s at 45°. Ignoring air, find the range and time of flight (g = 9.81 m/s²).
R = u² sin2θ ÷ g = 225 × sin90° ÷ 9.81 = 225 ÷ 9.81 ≈ 22.9 m. t = 2u sinθ ÷ g = 2 × 15 × 0.707 ÷ 9.81 ≈ 2.16 s.
7. Why does a shot-putter use about 38°–42° rather than 45°?
The shot is released about 2 m above the ground, so it lands lower than it started; a slightly flatter angle uses that extra fall time. Also the thrower can push faster at a lower angle, and speed matters most.
Common mistakes
- Mixing up plane and axis. The axis is a line at right angles to the plane: the sagittal plane uses the frontal axis, not the sagittal axis.
- Naming lever class by what is at the end. Name it by what is in the MIDDLE: fulcrum = 1st, load = 2nd, effort = 3rd.
- Saying 45° is always the best projection angle. It is only best from ground level with no air; real throws, jumps and kicks use lower angles.
- Thinking a spinning body gains angular momentum when it tucks. Angular momentum stays the same; only the spin speed rises because moment of inertia falls.