A non-uniform rod of mass M, length L and linear mass density λ = 2x2 is at a rotational equilibrium, shown in the figure*. On the left, mass m1 is hanging from a distance r1 from the wedge. Additionally, r2 denotes the distance between the center of the mass of the rod and the wedge. Derive an algebraic representation for r2 ONLY as a function of M, L, and m1 showing the steps to get there. Hint: first, find Xcm and then find 2 relationships between r1 and r2 *Note: figure is not drawn to scale.
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 non-uniform rod of mass M, length L and linear mass density λ = 2x2 is at a
Derive an algebraic representation for r2 ONLY as a function of M, L, and m1 showing the steps to get there.
Hint: first, find Xcm and then find 2 relationships between r1 and r2
*Note: figure is not drawn to scale.
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