Paper 2 · Moments and Equilibrium
The banking angle θ of an aeroplane moving with speed v on a path of radius of curvature r is given as tanθ = v²/(rg). Checking this using base units, which statement is correct?
Atanθ is dimensionless, but v²/(rg) reduces to units of m s^-2 once the radius and gravitational acceleration are substituted, so the equation is not dimensionally consistent as printed.
Bv²/(rg) reduces to units of seconds, so the equation cannot be dimensionally correct.
Ctanθ is dimensionless, and v²/(rg) also reduces to a dimensionless quantity, so the equation is dimensionally consistent.
DBoth sides carry units of m s^-1, so the equation happens to be consistent by coincidence.
Explanation: tanθ is dimensionless. [v²/(rg)] = (m² s^-2)/(m · m s^-2) = dimensionless. Both sides match, so the equation is dimensionally consistent.
Derived from ZIMSEC Physics Paper 2, November 2002, Q1