A string is attached to the rim of a small hoop of radius r = 8.00x10-2 m and mass m = 0.180 kg and then wrapped several times around the rim. If the free end of the string is held in place and the hoop is released from rest and allowed to drop, as shown in the figure (Figure 1), calculate the angular speed and the translational speed of the rotating hoop after it has descended h = 0.750 m. Use g = 9.80 m/s? for the acceleration due to gravity. What are the initial and final kinetic energies (K; and K ) of the hoop? Express the initial and final kinetic energies symbolically in terms of the final velocity v and variables given in the problem introduction, separated by a comma. • View Available Hint(s) Π ΑΣφ ?

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.