Convert the following to units in which c = 1, expressing everything in terms of m and kg:
(a) Worked example: 10 J. In SI units, 10 J = 10 kgm2 s−2. Since c = 1, we have 1 s = 3 × 108 m, and so 1 s−2 = (9 × 1016)−1 m−2. Therefore we get 10 J = 10 kgm2 (9 × 1016)−1 m−2 = 1.1 × 10−16 kg. Alternatively, treat c as a conversion factor:
1 = 3 × 108 ms−1,
1 = (3 × 108)−1 m−1 s,
10 J = 10 kgm2 s−2 = 10 kgm2 s−2 × (1)2
= 10 kgm2 s−2 × (3 × 108)−2 s2 m−2
= 1.1 × 10−16 kg.
You are allowed to multiply or divide by as many factors of c as are necessary to cancel out the seconds.
(b) The power output of 100W.
(c) Planck's reduced constant, = 1.05 × 10−34 J s. (definition of in  terms of Planck's constant h: = h / 2π.)
(d) Velocity of a car, v = 30ms−1.
(e) Momentum of a car, 3 × 104 kgms−1.
(f) Pressure of one atmosphere = 105Nm−2.
(g) Density of water, 103 kgm−3.
(h) Luminosity flux 106 J s−1 cm−2.