Trivial Dimensions Flashcards
Energy comes in many different forms. Name the physical dimensions of energy.
[E] = ML2t-2
Many forms of energy consists of work, kinetic, potential, …….
Name the physical dimensions of Power.
[P] = [ML2t-3]
Using Dimensional Analysis, give the average power P(W,t) and instaneous power P(F,v).
P = W/t for average power and P = F · v
Name are the physical dimensions of the spring constant k.
[k] = [Mt-2]
Name the physical dimensions that Impusle should be in.
[J] = [F dt] = [MLt-1]
Name the physical dimension of angular velocity w(r,v). Use D.A. to give an equation.
[w] = [t-1]
w = dθ / dt = v / r
θ is dimensionless ⇒ [θ] = [1].
Using D.A., give the equation for radian measure s(r,θ).
s = rθ
The linear acceleration a of the point has both tangential and radial components. Using D.A. give both equations in magnitude, at(r,α) and ar(v,r).
at = α r
ar = v2 / r
Give the physical dimensions of Rotational Inertia and the governed equation I(m,r).
[I] = [ML2]
I = Σmiri2
Give the equation that governs Torque Tnet(I,α) in magnitude.
[T] = [ML2t-2]
⇒
T = Iα
What is the physical dimensions of the gravitational constant G?
[G] = [L3M-1t-2]
What is the physical dimension of frequency f? How is it related to period?
[f] = [t-1]
f = T-1
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.
[w] = [t-1] ⇒ w = (k / m)1/2
T = 2π/w
Considering a sinusoidal wave, give the k wave number and wave speed vwave(λ,f) = vwave(w, k) = vwave(λ, T).
k = 2π / k
vwave = w / k = λ / T = λ f.
What are the physical dimensions of I(P, A) Intensity and governing equaiton?
[I] = [Mt-2]
I = P / A.
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?
v = (β/ρ)1/2
What are the physical dimensions of the bulk modulus β?
[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.
What is the physical dimension of L luminosity?
[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.
This base quantity is the rate at which charge passes a point.
What is current?
[I] = [ampere] = [A].
Name the physical dimensions of E the electric field strength.
[E] = [MLT-3I-1]
Give the electric potential’s V physical dimensions.
[V] = [volt] = [J/C] = [ML2I-1t-3]
Give physical dimensions of capacitance and using D.A. find the equation C(q,V).
[C] = [farads] = [C/V] = [1/J] = [M-1L-2t4I2]
C = q / v
Give the physical dimensions of pressure.
[P] = [pascals] = [ML-1T-2].
Give the physical dimensions of resistance.
R = [Ω] = [V/A] = [J/CA] = [ML2t-3I-2].