Ask Question
23 January, 10:11

A student sits on a rotating stool holding two 5 kg objects. When his arms are extended horizontally, the objects are 1.1 m from the axis of rotation, and he rotates with angular speed of 0.73 rad/sec. The moment of inertia of the student plus the stool is 2 kg m^2 and is assumed to be constant. The student then pulls the objects horizontally to a radius 0.31 m from the rotation axis.

(a) Calculate the final angular speed of the student. Answer in units of rad/s.

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

+4
Answers (1)
  1. 23 January, 12:17
    0
    Given that,

    Two object of Mass = 5kg

    M1 = M2 = 5kg

    Radius of rotation r = 1.1m

    Angular speed wi = 0.73rad/s

    Moment of inertia I = 2kgm²

    The student pull the mass to another position of r' = 0.31m

    A. Final angular momentum?

    Using the conservation of angular momentum

    The momentum of inertia of the objects the students holding I = mr²

    L (initial) = L (final)

    I•wi = I•wf

    (I+mr²+mr²) •wi = (I+mr'²+mr'²) •wf

    (2+5•1.1²+5•1.1²) •0.73 = (2+5•0.31²+5•0.31²) wf

    10.293 = 2.961wf

    Then, wf = 10.293/2.961

    wf = 3.476 rad/s

    wf ≈ 3.48rad/s

    b) kinetic energy before and after

    Kinetic energy is give as

    Kinetic energy = ½•I•w²

    Initial kinetic energy is

    K. E (initial) = ½ (I+mr²+mr²) wi²

    K. E (initial) = ½ (2+5•1.1²+5•1.1²) •0.73²

    K. E (initial) = 3.76 J

    Final kinetic energy is

    K. E (final) = ½ (I+mr'²+mr'²) wf²

    K. E (final) = ½ (2+5•0.31²+5•0.31²) 3.48²

    K. E (final) = 17.93J
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A student sits on a rotating stool holding two 5 kg objects. When his arms are extended horizontally, the objects are 1.1 m from the axis ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers