- #1
e2m2a
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Suppose I perform an experiment, set up as follows: There is a rotating body which rotates around a vertical axis. The axis is at one end of the rotating body (denoted as the rotator) so that the axis is not through the center of mass of the rotator. The vertical axis is attached to a second body, denoted as the slider. The slider is constrained to move along
a linear track with one degree of freedom. It moves parallel to the x-axis of an x-y coordinate system. At some prior time the center of mass of the rotator-slider system is determined by a balancing measurment, and a red circle is placed on the rotator at the exact center of mass of the rotator-slider system.
Initially, the rotator is parallel to the y-axis or at the "12 o'clock" position. We apply a force in the negative x-direction on the rotator. The slider is in contact with a left bumper, such that it cannot move to the left when the force is applied. After the force or torque is applied through an angular displacement, that is, we do initial work on the rotator, the rotator rotates at a constant angular velocity in the counter-clockwise direction. When the rotator is at the 5 o'clock position, we apply a second short outward radial force on the rotator, being careful that the force is always on the same line that goes through the axis of rotation and the center of mass of the rotator.
While all of this is happening, a high-speed video camera records the motion of the center of mass of the system, (the red circle). Analysis shows that after the initial force on the rotator, the speed of the red circle or the center of mass of the system remains constant until it reaches its 5 o'clock position. However, during the time the second outward radial force is applied, beginning at the 5 o'clock position, the speed of the center of mass increases. And after we stop applying the second force, the high speed video camera reveals that the speed of the center of mass(red circle) is greater than the initial speed of the center of mass. This may seem like a dumb question, but why did the speed of the center of mass of the system increase? And does this imply that the second force did work on the system, increasing its kinetic energy?
a linear track with one degree of freedom. It moves parallel to the x-axis of an x-y coordinate system. At some prior time the center of mass of the rotator-slider system is determined by a balancing measurment, and a red circle is placed on the rotator at the exact center of mass of the rotator-slider system.
Initially, the rotator is parallel to the y-axis or at the "12 o'clock" position. We apply a force in the negative x-direction on the rotator. The slider is in contact with a left bumper, such that it cannot move to the left when the force is applied. After the force or torque is applied through an angular displacement, that is, we do initial work on the rotator, the rotator rotates at a constant angular velocity in the counter-clockwise direction. When the rotator is at the 5 o'clock position, we apply a second short outward radial force on the rotator, being careful that the force is always on the same line that goes through the axis of rotation and the center of mass of the rotator.
While all of this is happening, a high-speed video camera records the motion of the center of mass of the system, (the red circle). Analysis shows that after the initial force on the rotator, the speed of the red circle or the center of mass of the system remains constant until it reaches its 5 o'clock position. However, during the time the second outward radial force is applied, beginning at the 5 o'clock position, the speed of the center of mass increases. And after we stop applying the second force, the high speed video camera reveals that the speed of the center of mass(red circle) is greater than the initial speed of the center of mass. This may seem like a dumb question, but why did the speed of the center of mass of the system increase? And does this imply that the second force did work on the system, increasing its kinetic energy?