Your town celebrates the 4 th of July with fireworks and asks you to design a di
ID: 1456885 • Letter: Y
Question
Your town celebrates the 4th 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 wheel (hoop) is I = MR2; we treat the rockets as point particles. Please be sure to use correct units.
Your town celebrates the 4th 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 wheel (hoop) is I = MR2; we treat the rockets as point particles. Please be sure to use correct units.
Explanation / Answer
a) I = M*R^2 + 4*m*R^2
= 0.6*0.5^2 + 4*0.1*0.5^2
= 0.25 kg.m^2
b)
KE = (1/2)*I*w^2 = (1/2)*0.25*10^2 = 12.5 J
angular momentum, L = I*w = 0.25*10 = 2.5 kg.m^2/s
c) Apply, Torque = I*alfa
= I*dw/dt
= 0.25*10/0.5
= 5 N.m
d) T = 4*F*R
==> F = T/(4*R)
= 5/(4*0.5)
= 5/2
= 2.5 N
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