Consider a cylindrical turntable whose mass is M and radius is R, turning with an initial angular speed ω1. (a) A parakeet of mass m, after hovering in flight above the outer edge of the turntable, gently lands on it and stays in one place on it, as shown below. What is the angular speed of the turntable after the parakeet lands? (Use any variable or symbol stated above as necessary.) (b) Becoming dizzy, the parakeet jumps off (not flies off) with a velocity relative to the turntable. The direction of is tangent to the edge of the turntable and in the direction of its rotation. What will be the angular speed of the turntable afterwards? Express your answer in terms of the two masses m and M, the radius R, the parakeet speed and the initial angular speed ω1. (Use any variable or symbol stated above along with the following as necessary: v for ||.)
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).
Consider a cylindrical turntable whose mass is M and radius is R, turning with an initial angular speed ω1.
(a) A parakeet of mass m, after hovering in flight above the outer edge of the turntable, gently lands on it and stays in one place on it, as shown below. What is the angular speed of the turntable after the parakeet lands? (Use any variable or symbol stated above as necessary.)
(b) Becoming dizzy, the parakeet jumps off (not flies off) with a velocity relative to the turntable. The direction of is tangent to the edge of the turntable and in the direction of its rotation. What will be the angular speed of the turntable afterwards? Express your answer in terms of the two masses m and M, the radius R, the parakeet speed and the initial angular speed ω1. (Use any variable or symbol stated above along with the following as necessary: v for ||.)
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