A rigid body consists of three thin uniform rods, each of mass m and length 2a, held mutually perpendicular at their midpoints. Choose a coordinate system with axes along the rods. (a) Find the angular momentum and kinetic energy of the body if it rotates with angular velocity cc about an axis passing through the origin and the point (1, 1, 1). (b) Show that the moment of inertia is the same for any axis passing through the origin. (e) Show that the moment of inertia of a uniform square lamina is that given in Example 9.1.1 for any axis passing through the center of the lamina and lying in the plane of the lamina
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).
A rigid body consists of three thin uniform rods, each of mass m and length 2a, held mutually perpendicular at their midpoints. Choose a coordinate system with axes along the rods.
(a) Find the
(b) Show that the moment of inertia is the same for any axis passing through the origin.
(e) Show that the moment of inertia of a uniform square lamina is that given in Example 9.1.1 for any axis passing through the center of the lamina and lying in the plane of the lamina
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