Question

5. Yo-Yo Pa, the grandmaster champion of the Yo-Yo wotld, per forms an "Around the world" where his yo-yo travels in a vertical circle. At the bottom, the yo-yo has an angular velocity of 8.72 rad/s. As it travels up the arc, the yo-yo loses angular velocity. At the top of its arc, the yo-yo has an angular velocity of 6.28 rad/s. You may treat the yo-yo as a point particle of unknown mass. (a) Explain briefly, using a conserved quantity, why the yo-yo has a smaller angular velocity at the top of its are. (b) What is the length of the yo-yo string? (e) He performs the same trick with a more massive yo-yo. The angular velocity at the bottom of the arc is the same as it was for the lighter yo-yo. How will the angular velocity at the top of the arc for the heavier yo-yo compare to that of the lighter yo-yo? Explain.

Answer 1

C) As you can see in the calculations that the mass is getting canceled out. So mass doesn't affect the velocities of an object. So performing experiment with heavier mass will give the exact same results.

W_1 = 8. 72 red/s so, velocity at A v_1 = w_1 R w_2 = 6. 28 red/s & v_2 = w_2 R Have, the conserved quantity is Mechanical Energy which is the addition of potential energy and kinetic energy so P. E + K. E = constant At point B, potential energy increases so, in order to keep the addition castanet kinetic energy has to decease Let potential at A in zero so by energy conservation k E_A + P E_A = k E_B + P E_B 1/2 m v^2_1 + 0 = 1/2 m v^2_2 + mg 2 R 1/2 (v^2_1 - v^2_2) = 2 g R w^2_1 R^2 - w^2_2 R^2 = 4 g R R = 4 g/w^2_1 - w^2_2 = 4 times 9. 8/(8. 72)^2 - (6. 28)^2 Length of string R = 1. 07 m