There are three masses, M1 = 1 kg, M2 = 3 kg, and M3 = 5 kg. M1 is located at (0,0); M2 is located at (2, 0); and M3 is located at (1, 1). (All positions are in meters.) Find the center-of-mass of this system of masses, with respect to the origin. Express your answer in unit vector notation, i.e., rcm = xcmi + ycmj where r, i, and j are vectors.
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).
There are three masses, M1 = 1 kg, M2 = 3 kg, and M3 = 5 kg. M1 is located at (0,0); M2 is located at (2, 0); and M3 is located at (1, 1). (All positions are in meters.) Find the center-of-mass of this system of masses, with respect to the origin. Express your answer in unit vector notation, i.e.,
rcm = xcmi + ycmj
where r, i, and j are vectors.
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