A student sits on a rotating stool holding two 2.8-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 2.8-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.50 m from the rotation axis.

(a) Find the new angular speed of the student.
  rad/s

(b) Find the kinetic energy of the student before and after the objects are pulled in.

Explanation / Answer

Moment of inertia (MI) at start = 3 + 2 x2.8 x12 = 8.6 kg m^2
Angular momentum ( L ) = Ix w= 8.6 x0.75 = 6.45 kg m^2 / s

MI at end = 3 + 2 x2.8x0.502 = 4.4 kgm^2

a) New angular velocity = 6.45 / 4.4 = 1.466 rad/s

b) Original KE = 1/2xMIxw2 = 0.5 x8.6x0.752 = 2.42 J

Final KE = 1/2x4.4x1.4662 = 4.728 J

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