Joule

Also called J

The SI unit of energy and work, symbol J, equal to one kilogram meter squared per second squared. One joule is the work done by a force of one newton acting through one meter along its own direction.

1 J=1 N⋅m=1 kg⋅m2s21\ \text{J} = 1\ \text{N}\cdot\text{m} = 1\ \frac{\text{kg}\cdot\text{m}^2}{\text{s}^2}

The first form follows from W=F∥dW = F_{\parallel}d, the second from substituting the newton. Every form of energy in AP Physics is measured in it: kinetic, potential, work, heat, internal energy. All four tables of information list joule, J, in their UNIT SYMBOLS box.

How big is one. About the work of lifting a 100 g apple one meter, (0.100)(9.8)(1.0)=0.98(0.100)(9.8)(1.0) = 0.98 J. A 1.0 kg object moving at 1.4 m/s carries about the same in kinetic energy.

The trap this entry exists for: torque is also newton metres, and torque is never written in joules. τ=r⊥F\tau = r_{\perp}F and W=F∥dW = F_{\parallel}d reduce to identical base units, so dimensional analysis cannot tell them apart. The geometry can. Work multiplies a force by a distance measured along the force; torque multiplies it by a distance measured perpendicular to the force. Different constructions, so the SI convention reserves the joule for energy and leaves torque in N⋅m\text{N}\cdot\text{m}. Writing a torque as 12 J is wrong even though 12 N times 1 m is 12 of something.

Rotational work does come out in joules, because W=τ ΔθW = \tau\,\Delta\theta multiplies newton metres by radians and the radian carries no dimensions.

One conversion worth knowing. The AP Physics 2 and C: Electricity and Magnetism constants boxes print 1 eV=1.60×10−19 J1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}, which is why particle energies get quoted in electron volts instead.

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