emz asked in Science & MathematicsPhysics · 1 decade ago

Motion of object, angular speed, and amount of work done?

A woman whose mass is 54.7 kg stands at the rim of a horizontal turntable which has a moment of inertia of

338 kg m^2 about the axis of rotation and a radius of 2.26 m. The system is initially at rest and the turntable is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim in a clockwise direction (viewed from above) at a constant speed of 0.873 m/s relative to the ground.

What will the motion of the turntable be, relative to the ground?

(pick best one)

1. at rest, non-rotating

2. rotating counterclockwise

3. rotating clockwise

What is its angular speed? Answer in units of rad/s.

How much work does the woman do to set the system into motion? Answer in units of J.

Update:

Which one is the angular speed? it's saying that 0.37 isn't correct, but that's how i worked it out as well

1 Answer

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  • odu83
    Lv 7
    1 decade ago
    Favorite Answer

    Even though the woman does work on the system the system will obey conservation of momentum.

    So Lw+Lt=0

    where Lw is the angular momentum of the woman and Lt is the angular momentum of the turntable.

    since Lw=-Lt and

    L=I*w

    then the turntable rotates counter clockwise.

    we know here angular speed to be

    .873/2.26

    =0.386 rad/sec

    I will treat her moment of inertia as a point mass

    54.7*2.26=338*w

    where w is the angular speed of the turntable

    w=54.7*2.26/338

    =0.366 rad/sec counter clockwise

    The energy can be calculated looking at the total rotational kinetic energy of the system.

    Rotational energy is

    .5*I*w^2

    since this is a magnitude, simply add the turntable and woman energy together

    .5*(54.7*2.26*0.386^2+

    338*0.366^2)

    =31.85 J

    j

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