Moment of Inertia
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Derive the Parallel Axis Theorem.
Derive the Perpendicular Axis Theorem.
Calculate the moment of inertia of a body of mass M relative to an axis at a distance D,
A system consists of two bodies of mass M and m (M>m) connected by a rod
of negligible mass, the distance between its centers is equal to R. Calculate the moment of
inertia relative to an axis passing through the center of mass of the system.
A system with four point bodies connected by bars of negligible mass, located at the corners of a square
of side R. Calculate the moment of inertia about an axis passing through the center of the square
and perpendicular to the plane containing the masses at the following cases:
a) The four bodies have masses equal to M;
b) The bodies have masses equal to 1 kg, 2 kg, 3 kg, 4 kg, and R = 2 m.
a) The four bodies have masses equal to M;
b) The bodies have masses equal to 1 kg, 2 kg, 3 kg, 4 kg, and R = 2 m.
A system has three masses connected by bars with negligible masses which are located at the points
indicated in the figure.
a) Calculate the position of the Center of Mass of this system;
b) Calculate the Moment of Inertia about the Center of Mass of the system.
The masses and positions of the bodies are: mA = 5 kg, (xA, yA) = (8, 0), mB = 7 kg, (xB, yB) = (–4, 6) and mC = 2 kg, (xC, yC) = (1, –2).
a) Calculate the position of the Center of Mass of this system;
b) Calculate the Moment of Inertia about the Center of Mass of the system.
The masses and positions of the bodies are: mA = 5 kg, (xA, yA) = (8, 0), mB = 7 kg, (xB, yB) = (–4, 6) and mC = 2 kg, (xC, yC) = (1, –2).
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