Your town celebrates the 4 h of July with fireworks and asks you to design a dis
ID: 1456362 • Letter: Y
Question
Your town celebrates the 4 h of July with fireworks and asks you to design a display. You envision a huge wheel with colorful rockets. To test your concept, you mount a bicycle wheel (radius R = 0.5 m, mass M = 0.6 kg) so that it is free to rotate about its axis; then you attach four small rockets (mass m = 0.1 kg) on the rim as shown in the figure. You want to fire the rockets to set the wheel spinning and spray colorful sparks. The moment of inertia of the w heel (hoop) is I = MR^2; we treat the rockets as point particles. Please be sure to use correct units. Calculate the moment of inertia of the object (wheel plus rockets) about the rotation axis. Calculate the kinetic energy and the angular momentum when the object is rotating with angular speed 10 rad/s. For the object starting from rest, calculate the average torque required to reach 10 rad/s in 0.5 seconds. Neglect any mass change of the rockets in this calculation. Mow much force must each rocket supply to produce this torque?Explanation / Answer
(a)
moment of inertia I = M*R^2 + 4*m*R^2 = (M+4m)*R^2
I = (0.6+(4*0.1))*0.5^2 = 0.25 kg m^2 <--------answer
(b)
KE = 0.5*I*w^2 = 0.5*0.25*10^2 = 12.5 J <--------answer
angular momentum L = I*w = 0.25*10 = 2.5 kg m^2/s <--------answer
(c)
angular acceleration alpha = (w2-w1)/t = (10-0)/0.5 = 20 rad's^2
torque = I*alpha = 0.25*20 = 5 Nm <--------answer
(d)
torque = R*F
5 = 0.5*F
F = 10 N <<--------answer
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