A large horizontal circular platform (M=93.8 kg, r=3.76 m) rotates about a frictionless vertical axle. A student (m=54.81 kg) walks slowly from the rim of the platform toward the center. The angular velocity ω of the system is 3.32 rad/s when the student is at the rim. Find the moment of inertia of platform through the center with respect to the z-axis. Find the moment of inertia of the student about the center axis (while standing at the rim) of the platform. Find the moment of inertia of the student about the center axis while the student is standing 1.84 m from the center of the platform.
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 large horizontal circular platform (M=93.8 kg, r=3.76 m) rotates about a frictionless vertical axle. A student (m=54.81 kg) walks slowly from the rim of the platform toward the center. The
Find the moment of inertia of platform through the center with respect to the z-axis.
Find the moment of inertia of the student about the center axis (while standing at the rim) of the platform.
Find the moment of inertia of the student about the center axis while the student is standing 1.84 m from the center of the platform.
Find the angular speed when the student is 1.84 m from the center of the platform.
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