Find the center of mass of a sphere of mass M and radius R and a cylinder of mass m, radius r, and height h arranged as shown below. Express your answers in a coordinate system that has the origin at the center of the cylinder. (Assume that the +x-axis is to the right, the +y-axis is up along the page, and the +z-axis is out of the page. Use any variable or symbol stated above as necessary.) a) xCM=___, yCM=___, zCM=___ b) xCM=___, yCM=___, zCM=___
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).
Find the center of mass of a sphere of mass M and radius R and a cylinder of mass m, radius r, and height h arranged as shown below. Express your answers in a coordinate system that has the origin at the center of the cylinder. (Assume that the +x-axis is to the right, the +y-axis is up along the page, and the +z-axis is out of the page. Use any variable or symbol stated above as necessary.)
a) xCM=___, yCM=___, zCM=___
b) xCM=___, yCM=___, zCM=___
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