For a cylinder of height h and radius r2, the density from the center to r1 is constant p1, the density between r1 and r2 is constant p2. Find the moment of inertia of the cylinder about an axis of rotation parallel to the axis of symmetry and at a distance d from the axis of symmetry. Give your answer in terms of (h, r1, r2, p1, p2 and d) Hint is given in the 2. figure At the end of this problem, you will need to use the Parallel Axis Theorem.
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
For a cylinder of height h and radius r2, the density from the center to r1 is constant p1, the density between r1 and r2 is constant p2.
Find the moment of inertia of the cylinder about an axis of rotation parallel to the axis of symmetry and at a distance d from the axis of symmetry.
Give your answer in terms of (h, r1, r2, p1, p2 and d)
Hint is given in the 2. figure
At the end of this problem, you will need to use the Parallel Axis Theorem.
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