Conservation of Angular Momentum Given data on two disks, such as masses and inner/outer diameters/radii, and the initial angular velocities of the 2 disks, use the conservation of angular momentum principle to calculate the common angular velocity after the two disks are allowed to contact each other and spin together. Or, given the common final angular velocity, solve for unknowns such as the initial angular velocity of one of the disks. Or, given data on the starting and final angular velocities and some data on the disks, solve for unknowns such as moments of inertia, masses or diameters/radii. EXAMPLE Two metal disks have masses m1=3.45 kg and m2=UNKNOWN kg, and each has a radius of 8.31 cm. (You may ignore the inner hole for both disks - assume that it is very small.) They spin on cushions of air in a standard rotational dynamics apparatus. Initially, disk #1 is spinning counterclockwise at 6.02 rad/s and disk #2 is spinning clockwise at 2.50 rad/s. A pin is removed that drops disk #1 onto disk #2. After a short time they are seen to spin at the same angular speed of 2.33 rad/s, counterclockwise. Assume that there are no outside frictional forces acting on the system of the two disks. a. Calculate the moment of inertia of the first disk. Include units. (0.0119 kg m²) b. Calculate the mass of the second disk in this ideal situation. Include units. (2.63 kg)
Conservation of Angular Momentum Given data on two disks, such as masses and inner/outer diameters/radii, and the initial angular velocities of the 2 disks, use the conservation of angular momentum principle to calculate the common angular velocity after the two disks are allowed to contact each other and spin together. Or, given the common final angular velocity, solve for unknowns such as the initial angular velocity of one of the disks. Or, given data on the starting and final angular velocities and some data on the disks, solve for unknowns such as moments of inertia, masses or diameters/radii. EXAMPLE Two metal disks have masses m1=3.45 kg and m2=UNKNOWN kg, and each has a radius of 8.31 cm. (You may ignore the inner hole for both disks - assume that it is very small.) They spin on cushions of air in a standard rotational dynamics apparatus. Initially, disk #1 is spinning counterclockwise at 6.02 rad/s and disk #2 is spinning clockwise at 2.50 rad/s. A pin is removed that drops disk #1 onto disk #2. After a short time they are seen to spin at the same angular speed of 2.33 rad/s, counterclockwise. Assume that there are no outside frictional forces acting on the system of the two disks. a. Calculate the moment of inertia of the first disk. Include units. (0.0119 kg m²) b. Calculate the mass of the second disk in this ideal situation. Include units. (2.63 kg)
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Question
Transcribed Image Text:Conservation of Angular Momentum
Given data on two disks, such as masses and inner/outer diameters/radii, and
the initial angular velocities of the 2 disks, use the conservation of angular
momentum principle to calculate the common angular velocity after the two
disks are allowed to contact each other and spin together.
Or, given the common final angular velocity, solve for unknowns such
as the initial angular velocity of one of the disks.
Or, given data on the starting and final angular velocities and some
data on the disks, solve for unknowns such as moments of inertia, masses or
diameters/radii.
EXAMPLE
Two metal disks have masses m1=3.45 kg and m2=UNKNOWN kg, and
each has a radius of 8.31 cm. (You may ignore the inner hole for both disks
assume that it is very small.) They spin on cushions of air in a standard
rotational dynamics apparatus. Initially, disk #1 is spinning
counterclockwise at 6.02 rad/s and disk #2 is spinning clockwise at 2.50
rad/s. A pin is removed that drops disk #1 onto disk #2. After a short time
they are seen to spin at the same angular speed of 2.33 rad/s,
counterclockwise. Assume that there are no outside frictional forces acting
on the system of the two disks.
a. Calculate the moment of inertia of the first disk. Include units.
(0.0119 kg m²)
b. Calculate the mass of the second disk in this ideal situation. Include units.
(2.63 kg)
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Step 1: Computing the relation of moment of inertia of the first and second disk respectively:
VIEWStep 2: Calculating the moment of inertia of the first disk:
VIEWStep 3: Computing the relation of moment of inertia of the second disk:
VIEWStep 4: Finding the value of the moment of inertia of the second disk:
VIEWStep 5: Finding the value of the mass of the second disk in the ideal situation:
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