Consider a cylindrical turntable whose mass is M and radius is R, turning with a

Question

Consider a cylindrical turntable whose mass is M and radius is R, turning with an initial angular speed 1.

(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.) f =

(b) Becoming dizzy, the parakeet jumps off (not flies off) with a velocity vector v relative to the turntable. The direction of vector v 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 1. (Use any variable or symbol stated above along with the following as necessary: v for |vector v|.) f =

Explanation / Answer

a)

It = moment of inertia of cylinderical turntable = (0.5) MR2

Wi = initial angular velocity = W1

Using conservation of angular momentum

It Wi = (It + mR2) Wf

(0.5) MR2 W1 = ((0.5) MR2 + mR2) Wf

Wf = (0.5) MR2 W1 / ((0.5) MR2 + mR2)

b)

Wpt = angular velocity of parakeet relative to turntable

Wpg = angular velocity of parakeet relative to ground

Wtg = angular velocity of turntable relative to ground

Wpt = Wpg - Wtg

V/R + Wf = Wpg   

Vpg = RWpg                

Vpg = V + RWf                   eq-1

Using conservation of angular momentum

((0.5) MR2 + mR2) Wf = m Vpg R + It Wf'

(0.5) MR2 W1 = m (V + RWf ) R + (0.5) MR2 Wf'

2 [(0.5) MR2 W1 - m (V + RWf ) R ] / (MR2 ) = Wf'

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.