Motion in a Plane - Quick Revision
Vectors
- Scalar: magnitude only; vector: magnitude + direction, obeys triangle/parallelogram law. Equal vectors: same magnitude AND direction.
- Addition commutative (A+B=B+A) and associative; A+(-A)=null vector. Subtraction: A-B=A+(-B).
- Unit vectors i,j,k (magnitude 1, dimensionless). Components: Ax=A cos theta, Ay=A sin theta, A=sqrt(Ax^2+Ay^2). (Ax is a number; Ax i is a vector.)
- Dot product A.B = AB cos theta (scalar). Cross product |AxB| = AB sin theta (vector, perpendicular).
Projectile motion
- Horizontal velocity constant (ax=0); vertical = free fall (ay=-g). Path = parabola.
- Time of flight T = 2 vo sin theta/g; max height H = (vo sin theta)^2/2g; range R = vo^2 sin 2theta/g (max at 45 deg, Rmax=vo^2/g). At the top, vy=0 (velocity horizontal). Horizontal & vertical motions independent.
Uniform circular motion
- Constant speed, changing velocity (direction) => acceleration. v=omega R; omega=2pi/T.
- Centripetal acceleration a = v^2/R = omega^2 R, directed toward the centre.