More practice questions

4. Q4. Angular momentum is L = mvr for a particle of mass m moving with speed v on a circle of radius r. Find its dimensions.

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   [mvr] = [M] × [L T^⁻¹] × [L] = [M L^² T^⁻¹]. (The italic L is the symbol for angular momentum; the upright [L] is the dimension of length.)

5. Q5. The energy of a photon is E = hν, where ν is its frequency. Find the dimensions of the Planck constant h, and name a mechanical quantity with the same dimensions.

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   h = E/ν, so [h] = [M L^² T^⁻²]/[T^⁻¹] = [M L^² T^⁻¹]. Angular momentum (Q4) has the same dimensions.

6. Q6. The coefficient of viscosity η is defined by F = ηA(v/l), where F is a force, A an area and v/l a velocity gradient. Find the dimensions of η.

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   η = Fl/(Av), so

   [η] = [M L T^⁻²] × [L]/([L^²] × [L T^⁻¹])

   = [M L^² T^⁻²]/[L^³ T^⁻¹]

   = [M L^⁻¹ T^⁻¹].