Rewrite the conservation of energy equation,mgyi = ½ mvf^2 + ½ Iωf^2, so that it uses the appropriate moment of inertia for either the sphere or the cylinder. Use the fact that ωr = v to eliminate ω and r from the equation and cancel out the masses and solve for vf. Sphere: I = 2/5mr^2 Cylinder: I = 1/2mr^2
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).
Rewrite the conservation of energy equation,mgyi = ½ mvf^2 + ½ Iωf^2, so that it uses the appropriate moment of inertia for either the sphere or the cylinder. Use the fact that ωr = v to eliminate ω and r from the equation and cancel out the masses and solve for vf.
Sphere: I = 2/5mr^2
Cylinder: I = 1/2mr^2
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