Two lops (#1 and #2) spin with angular velocities of omega_1 = 43 rad/s and omeg

Question

Two lops (#1 and #2) spin with angular velocities of omega_1 = 43 rad/s and omega_2 = 67 rad/s, respectively, in opposite senses about vertical axes on a table. They briefly collide, and, alter the collision, the first top is spinning at 23 rad/s in the same sense as it was before the collision. Assuming that I_1 = 0.48 * I_2 (I: rotational inertia) (a) Determine the magnitude and sense of the final angular velocity of the second top. (b) If the collision lasts for 0.050 s what is the torque exerted on #1 top by #2 top? (c) Was the kinetic energy of the system conserved or not during this collision? Justify your answer with the appropriate calculations.

Explanation / Answer

Here,

a) Using conservation of angular momentum

I1 * w1 + I2 * w2 = I1 * wf1 + I2 * wf2

43 * I2 * 0.48 + 67 * I2 = 23 * 0.48 * I2 + I2 * wf2

wf2 = 76.6 rad/s

the final angular velocity of the second top is 76.6 rad/s

b)

for the torque

torque acting on the top 1 by top 2 = change in angular momentum/time

torque acting on the top 1 by top 2 = I1 * (43 - 23)/0.050

torque acting on the top 1 by top 2 = 400 * I1

c)

the kinetic energy during this collision is not constant

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