Trivial Dimensions

Question 1

Energy comes in many different forms. Name the physical dimensions of energy.

Answer 1

[E] = ML²t^-2

Many forms of energy consists of work, kinetic, potential, …….

Question 2

Name the physical dimensions of Power.

Answer 2

[P] = [ML²t^-3]

Question 3

Using Dimensional Analysis, give the average power P(W,t) and instaneous power P(F,v).

Answer 3

P = W/t for average power and P = F · v

Question 4

Name are the physical dimensions of the spring constant k.

Answer 4

[k] = [Mt^-2]

Question 5

Name the physical dimensions that Impusle should be in.

Answer 5

[J] = [F dt] = [MLt^-1]

Question 6

Name the physical dimension of angular velocity w(r,v). Use D.A. to give an equation.

Answer 6

[w] = [t^-1]

w = dθ / dt = v / r

θ is dimensionless ⇒ [θ] = [1].

Question 7

Using D.A., give the equation for radian measure s(r,θ).

Answer 7

s = rθ

Question 8

The linear acceleration a of the point has both tangential and radial components. Using D.A. give both equations in magnitude, a_t(r,α) and a_r(v,r).

Answer 8

a_t = α r

a_r = v² / r

Question 9

Give the physical dimensions of Rotational Inertia and the governed equation I(m,r).

Answer 9

[I] = [ML²]

I = Σm_ir_i²

Question 10

Give the equation that governs Torque T_net(I,α) in magnitude.

Answer 10

[T] = [ML²t^-2]

⇒

T = Iα

Question 11

What is the physical dimensions of the gravitational constant G?

Answer 11

[G] = [L³M^-1t^-2]

Question 12

What is the physical dimension of frequency f? How is it related to period?

Answer 12

[f] = [t^-1]

f = T^-1

Question 13

A particle with mass m that moves under the influence of a Hooke’s law restoring force given by F = -kx exhibits harmonic motion with w(k,m) angular frequency and T(m,k) period. Give the physical dimensions and using D.A. give these equations.

Answer 13

[w] = [t^-1] ⇒ w = (k / m)^1/2

T = 2π/w

Question 14

Considering a sinusoidal wave, give the k wave number and wave speed v_wave(λ,f) = v_wave(w, k) = v_wave(λ, T).

Answer 14

k = 2π / k

v_wave = w / k = λ / T = λ f.

Question 15

What are the physical dimensions of I(P, A) Intensity and governing equaiton?

Answer 15

[I] = [Mt^-2]

I = P / A.

Question 16

Sound waves are longitudinal mechanical waves that can travel through solids, liquids, or gases. The speed v of a sound wave in a medium having bulk modulus β and density ρ is what?

Answer 16

v = (β/ρ)^1/2

Question 17

What are the physical dimensions of the bulk modulus β?

Answer 17

[β] = [N/m²] = [Pascals] = [ML^-1t²]

The bulk modulus is the property that determines the extent to which an element of a medium changes in volume when the pressure on it changes.

Question 18

What is the physical dimension of L luminosity?

Answer 18

[L] = [Power] = [ML²t^-3] = [candela].

Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object.

In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical object.

Question 19

This base quantity is the rate at which charge passes a point.

Answer 19

What is current?

[I] = [ampere] = [A].

Question 20

Name the physical dimensions of E the electric field strength.

Answer 20

[E] = [MLT^-3I^-1]

Question 21

Give the electric potential’s V physical dimensions.

Answer 21

[V] = [volt] = [J/C] = [ML²I^-1t^-3]

Question 22

Give physical dimensions of capacitance and using D.A. find the equation C(q,V).

Answer 22

[C] = [farads] = [C/V] = [1/J] = [M^-1L^-2t⁴I²]

C = q / v

Question 23

Give the physical dimensions of pressure.

Answer 23

[P] = [pascals] = [ML^-1T^-2].

Question 24

Give the physical dimensions of resistance.

Answer 24

R = [Ω] = [V/A] = [J/CA] = [ML²t^-3I^-2].

Question 25

In a resistor, electric potential energy is converted to internal thermal energy via collisions between charge carriers and atoms. A measurement of this is called resistive dissipation, P(i,R) or P(V,R). Using D.A., find both equations.

Answer 25

P = i²R and P = V²/R.

Question 26

Give the physical dimensions of B the magnetic field.

Answer 26

[B] = [Tesla] = [N(Am)^-1] = [IL^-1].

Question 27

An inductor is a device that can be used to produce a known magnetic field in a specified region. Give the physical dimensions of inductance L.

Answer 27

[L] = [henry] = [T·m²/A] = [Nm/A²] = [ML²T^-2I^-2].

Question 28

Give the physical dimensions of ρ electric charge density.

Answer 28

[ρ] = [L^-3TI]

Question 29

Give the physical dimensions of Φ_B the magnetic flux.

Answer 29

[Φ_B] = [weber] = [T·m²] = [ML²T^-2I^-1].

Question 30

Give the physical dimensions of Φ_E the electric flux.

Answer 30

[Φ_E] = [(volt/m)·m²] = [ML³T^-3I^-1].

Question 31

The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current (such as electromagnets), permanent magnets, moving elementary particles (such as electrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc). Give the physical dimensions of m the magnetic moment.

Answer 31

[m] = [A·m²] = [L²I].

Question 32

The permittivity of free space, ε₀, is a physical constant used often in electromagnetism. It represents the capability of a vacuum to permit electric fields. It is also connected to the energy stored within an electric field and capacitance. Perhaps more surprisingly, it’s fundamentally related to the speed of light. Give the physical dimensions of ε₀.

Answer 32

[ε₀] = [Farad·m^-1] = [M^-1L^-3T⁴I²].

Question 33

The permeability of free space, μ₀, is a physical constant used often in electromagnetism. t is connected to the energy stored in a magnetic field, the speed of light and permittivity of free space. Give the physical dimensions of μ₀.

Answer 33

[μ₀] = [H·m^-1] = [MLT^-2I^-2].