Forces, Movement & Changing Shape

Definitions

• A scalar quantity has a magnitude only, so it is described fully by a number with a unit
• A vector quantity has both a magnitude and a direction, so it is only described fully when both are stated

Distance and displacement

• Distance is how far an object has actually travelled along its path, ignoring direction; distance is therefore a scalar
• Displacement is the straight-line gap between the start point and the end point of the motion, together with the direction from start to end; displacement is therefore a vector
• On a route with bends, distance and displacement give different numerical answers, because the distance grows with every twist while the displacement only depends on where you end up

Speed and velocity

• Speed is the rate at which distance is covered, so it is a scalar
• Velocity is the rate at which displacement is covered, and includes a direction, so it is a vector
• An object moving at a steady speed around a circle has a continually changing velocity (because the direction keeps changing) even though the speed stays the same

Common pairs

Representing forces with arrows

• Forces are drawn as arrows on a free-body diagram:
  • the length of each arrow scales with the size of the force it represents (a 6 N arrow comes out twice as long as a 3 N arrow on the same diagram)
  • the direction the arrow points shows the line of action of the force
  • each arrow is labelled with the name of the force or with its size in newtons (e.g. W for weight, or "75 N pull")
• Forces that point neither straight up nor straight along the ground are described by stating the angle from the horizontal or from the vertical (e.g. "a 60 N force acting at 30° above the horizontal")