Angular momentum

Rolling ball has both linear momentum and angular momentumA rolling ball has both linear momentum and angular momentum. The linear momentum is the product of mass and translational velocity, as you learned on page 613. Angular momentum is a different kind of momentum, with different units that obeys a separate conservation law. Any moving mass has both angular momentum and linear momentum. The quantity of angular momentum depends on the choice of center of rotation as well as the mass and velocity. Read the text aloud
Mass on a string swung overhead has both linear momentum and angular momentumAngular momentum is associated with the movement of mass about a particular axis of rotation. Imagine spinning a mass attached to a string around over your head. At any given moment, the mass m is moving with a velocity v, so it has a linear momentum p = mv. As it spins over your head, the same mass has an angular momentum (denoted with the letter L). Angular momentum is equal to the radius of rotation times the linear momentum, or L = r×mv. Note that the same mass moving at the same velocity may have a different angular momentum about a different center. Read the text aloud
(13.2) L=r×mv
L  = angular momentum (kg m2/s)
r  = radius from axis (m)
m  = mass (kg)
v  = velocity (m/s)
Angular momentum
for a point mass
Angular momentum and linear momentum have different units! The units of linear momentum are kg m/s. When we calculate angular momentum we multiply linear momentum by distance, so angular momentum has units of kg m2/s. Read the text aloud Show Is angular momentum a scalar or vector quantity?
Rotational and orbital angular momentumAn object can have multiple quantities of angular momentum around multiple axes. For example, Earth has rotational angular momentum because of its rotation about its north–south axis. Earth also has orbital angular momentum because the planet revolves around its orbital axis passing through the Sun. Read the text aloud
Calculate the angular momentum of a 100 g mass revolving in a circle once per second at the end of a 0.75 m string.
Asked: angular momentum L
Given: mass m = 100 g = 0.1 kg, radius r = 0.75 m, ω = 1 rev/s
Relationships: angular momentum L = rmv
Solution: The mass moves 2πr every second, so its velocity is
v = distance/time = (2π)(0.75 m) ÷ (1 s) = 4.7 m/s
Its angular momentum is therefore
L = rmv = (0.75 m)(0.1 kg)(4.7 m/s) = 0.35 kg m2/s
Answer: The angular momentum is 0.35 kg m2/s.
Read the text aloud
If you double the mass of the object on a string that you are spinning around over your head, how will its angular momentum change? Show

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