Difference between revisions of "Angular Momentum"
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Angular momentum is related to linear momentum in that it measures the amount of motion in a body. Linear momentum measures the amount of linear motion, while angular momentum measures the amount of angular motion. | Angular momentum is related to linear momentum in that it measures the amount of motion in a body. Linear momentum measures the amount of linear motion, while angular momentum measures the amount of angular motion. | ||
| − | The equation for linear | + | The equation for linear momentum is mass times velocity, while for angular momentum it is moment of inertia times angular velocity (makes you wonder if mass = inertia?). Since nothing is ever at rest because there is no absolute zero-motion reference frame (as far as we know), everything has momentum, both linear and angular. |
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| + | Equations that show the relationship between linear and angular momentum: | ||
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| + | linear momentum = mv | ||
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| + | angular momentum = <span style="font-family:verdana;">I</span></span><span style="font-family:symbol;">w</span> | ||
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| + | force = F = ma | ||
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| + | torque = <span style="font-family:symbol;">t</span> = <span style="font-family:verdana;">I</span>*<span style="font-family:symbol;">a</span> | ||
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| + | linear kinetic energy = ½mv<sup>2</sup> | ||
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| + | angular kinetic energy = ½<span style="font-family:verdana;">I<span style="font-family:symbol;">w</span><sup>2</sup> | ||
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| + | ==abbreviations== | ||
| + | p = linear momentum | ||
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| + | L = angular momentum | ||
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| + | v = linear velocity | ||
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| + | <span style="font-family:symbol;">w</span> = angular velocity | ||
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| + | a = acceleration | ||
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| + | <span style="font-family:symbol;">a</span> = angular acceleration | ||
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| + | m = mass | ||
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| + | <span style="font-family:verdana;">I</span></span> = moment of inertia | ||
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| + | ==Application to Quantum Mechanics== | ||
Latest revision as of 03:20, 21 March 2020
Angular momentum is related to linear momentum in that it measures the amount of motion in a body. Linear momentum measures the amount of linear motion, while angular momentum measures the amount of angular motion.
The equation for linear momentum is mass times velocity, while for angular momentum it is moment of inertia times angular velocity (makes you wonder if mass = inertia?). Since nothing is ever at rest because there is no absolute zero-motion reference frame (as far as we know), everything has momentum, both linear and angular.
Equations that show the relationship between linear and angular momentum:
linear momentum = mv
angular momentum = Iw
force = F = ma
torque = t = I*a
linear kinetic energy = ½mv2
angular kinetic energy = ½Iw2
abbreviations
p = linear momentum
L = angular momentum
v = linear velocity
w = angular velocity
a = acceleration
a = angular acceleration
m = mass
I = moment of inertia
