1. A satellite is spinning at 6 rev/s. The satellite consists of a main body in the shape of a sphere of radius 3 m and a mass of 300 kg, and two antennas projecting out from the surface of the main body that can be approximated with rods of length 4 m each and mass 10 kg. The antennas lie in the plane of rotation. See the figure below. M, L Ms R M,L Things to think about: 1. The system is made of one sphere and two rods attached to the surface of the sphere. The total moment of inertia of the system is the sum of individual moments of inertia. 2. The axis of rotation for the system is about the center of the sphere. How can you calculate the moment of inetia of the rods about this axis? How far are the center of mass of the rods away from the axis of rotation? 3. What is the moment of inertia of a rod about an axis through the center of the rod? (a) Calculate the total moment of intertia of the system about an axis passing through the center of the sphere. total kg m² (b) What is the magnitude of the angular momentum of the satellite? L=22368-139 kg m²/s
1. A satellite is spinning at 6 rev/s. The satellite consists of a main body in the shape of a sphere of radius 3 m and a mass of 300 kg, and two antennas projecting out from the surface of the main body that can be approximated with rods of length 4 m each and mass 10 kg. The antennas lie in the plane of rotation. See the figure below. M, L Ms R M,L Things to think about: 1. The system is made of one sphere and two rods attached to the surface of the sphere. The total moment of inertia of the system is the sum of individual moments of inertia. 2. The axis of rotation for the system is about the center of the sphere. How can you calculate the moment of inetia of the rods about this axis? How far are the center of mass of the rods away from the axis of rotation? 3. What is the moment of inertia of a rod about an axis through the center of the rod? (a) Calculate the total moment of intertia of the system about an axis passing through the center of the sphere. total kg m² (b) What is the magnitude of the angular momentum of the satellite? L=22368-139 kg m²/s
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:1. A satellite is spinning at 6 rev/s. The satellite consists of a main body in the shape of a sphere of
radius 3 m and a mass of 300 kg, and two antennas projecting out from the surface of the main body
that can be approximated with rods of length 4 m each and mass 10 kg. The antennas lie in the plane
of rotation. See the figure below.
M, L
Ms
R
M₁L
Things to think about:
1. The system is made of one sphere and two rods attached to the surface of the sphere. The
total moment of inertia of the system is the sum of individual moments of inertia.
2. The axis of rotation for the system is about the center of the sphere. How can you calculate
the moment of inetia of the rods about this axis? How far are the center of mass of the rods
away from the axis of rotation?
3. What is the moment of inertia of a rod about an axis through the center of the rod?
(a) Calculate the total moment of intertia of the system about an axis passing through the center of
the sphere.
Itotal
kg m²
(b) What is the magnitude of the angular momentum of the satellite?
L = 22368.139
kg m²/s
Transcribed Image Text:1) Angular momentum of a Satellite
f = 6 rev
S
1 = mr²
| Sphere = MR²
Irod = 1/2/2ML ²
10kg
-0) 2 = 1 total w
- 41720.350
4m
Grey ( 2 = rad ) = 12 = rad = W
S
Trev
300.0kg
(a)
2
I total = (300.0 mg) (3m)² + 2 ( 12 (10µg) (4m) ²)
=1106.666 kg.m²
3m
3m
Mgm²/s
Что
10 ng
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Follow-up Question
The moment of inertia of single rod about axis of sphere by using parallel axis theorem is given by:
IR = mL212+ m R+L22
Not sure what the equation means?
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