A 80 cm long metal bar with mass 40 grams is attached to a pivot with a massless string 60 cm long. Find the kinetic energy of the bar when it is rotated at a rate of 3 revolutions per second.

Answer 1

1. First, we need to calculate the inertia of the meta bar. At position x, the inertia is given by

m * dx/L * x**2

where m = 0.04, and L = 0.8

1. The total inertia can be obtained by integrating the equation above from 0.6 to 1.4, thus we get

I = 0.04/0.8 * 1/3 ( 1.4**3 - 0.6 ** 3) = 0.042

1. The angular speed w is given by 2 * pi * 3 = 18.84
2. The total kinetic energy is Iw² = 0.042 * 18.84² = 14.974 J