dimensions of moment of inertia
Answers
Answer:
Explanation:
Physical Quantities
Quantity Definition Formula Units Dimensions
Basic Mechanical Length or Distance fundamental d m (meter) L (Length)
Time fundamental t s (second) T (Time)
Mass fundamental m kg (kilogram) M (Mass)
Area distance2 A = d2 m2 L2
Volume distance3 V = d3 m3 L3
Density mass / volume d = m/V kg/m3 M/L3
Velocity distance / time v = d/t m/s
c (speed of light) L/T
Acceleration velocity / time a = v/t m/s2 L/T2
Momentum mass × velocity p = m·v kg·m/s ML/T
Force
Weight mass × acceleration
mass × acceleration of gravity F = m·a
W = m·g N (newton) = kg·m/s2 ML/T2
Pressure or Stress force / area p = F/A Pa (pascal) = N/m2 = kg/(m·s2) M/LT2
Energy or Work
Kinetic Energy
Potential Energy force × distance
mass × velocity2 / 2
mass × acceleration of gravity × height E = F·d
KE = m·v2/2
PE = m·g·h J (joule) = N·m = kg·m2/s2 ML2/T2
Power energy / time P = E/t W (watt) = J/s = kg·m2/s3 ML2/T3
Impulse force × time I = F·t N·s = kg·m/s ML/T
Action energy × time
momentum × distance S = E·t
S = p·d J·s = kg·m2/s
h (quantum of action) ML2/T
Rotational Mechanical Angle fundamental θ ° (degree), rad (radian), rev
360° = 2π rad = 1 rev dimensionless
Cycles fundamental n cyc (cycles) dimensionless
Frequency cycles / time f = n/t Hz (hertz) = cyc/s = 1/s 1/T
Angular Velocity angle / time ω = θ/t rad/s = 1/s 1/T
Angular Acceleration angular velocity / time α = ω/t rad/s2 = 1/s2 1/T2
Moment of Inertia mass × radius2 I = m·r2 kg·m2 ML2
Angular Momentum radius × momentum
moment of inertia × angular velocity L = r·p
L = I·ω J·s = kg·m2/s
ћ (quantum of angular momentum) ML2/T
Torque or Moment radius × force
moment of inertia × angular acceleration τ = r·F
τ = I·α N·m = kg·m2/s2 ML2/T2
Thermal Temperature fundamental T °C (celsius), K (kelvin) K (Temp.)
Heat heat energy Q J (joule) = kg·m2/s2 ML2/T2
Entropy heat / temperature S = Q/T J/K ML2/T2K
Electromagnetic Electric Charge +/- fundamental q C (coulomb)
e (elementary charge) Q (Charge)
Current charge / time i = q/t A (amp) = C/s Q/T
Voltage or Potential energy / charge V = E/q V (volt) = J/C ML2/QT2
Resistance voltage / current R = V/i Ω (ohm) = V/A ML2/Q2T
Capacitance charge / voltage C = q/V F (farad) = C/V Q2T2/ML2
Inductance voltage / (current / time) L = V/(i/t) H (henry) = V·s/A ML2/Q2
Electric Field voltage / distance
force / charge E = V/d
E = F/q V/m = N/C ML/QT2
Electric Flux electric field × area ΦE = E·A V·m = N·m2/C ML3/QT2
Magnetic Field force / (charge × velocity) B = F/(q·v) T (tesla) = Wb/m2 = N·s/(C·m) M/QT
Magnetic Flux magnetic field × area ΦM = B·A Wb (weber) = V·s = J·s/C ML2/QT
Note: Other conventions define different quantities to be fundamental.
Mass, energy, momentum, angular momentum, and charge are conserved, which means the total amount does not change in an isolated system.
Moment of Inertia mass × radius2 = ML2
then ,[ L2 M 1 T0 ]