a fireworks display uses a square 0.10m platform onwhich rocket tubes are placed

Question

a fireworks display uses a square 0.10m platform onwhich  rocket tubes are placed on each edge, as theyburn, the square spins about its axis perp. to itscenter. It reaches an angular speed of 31rad/s in 0.5s fromrest. 3 of the tubes has a force of 0.3 N each, the 4th isunknown. If the moment of inertia has a constant value fo0.001kg*m^2, what is the mag of the force of the 4th tube? need help setting up problem, is the radius 7.07? a fireworks display uses a square 0.10m platform onwhich  rocket tubes are placed on each edge, as theyburn, the square spins about its axis perp. to itscenter. It reaches an angular speed of 31rad/s in 0.5s fromrest. 3 of the tubes has a force of 0.3 N each, the 4th isunknown. If the moment of inertia has a constant value fo0.001kg*m^2, what is the mag of the force of the 4th tube? need help setting up problem, is the radius 7.07?

Explanation / Answer

The length of the platform used to display fireworks is L =0.10 m The angular speed of the square is w = 31 rad/s The square reaches the angular speed in a time t = 0.5 s fromrest 3 of the tubes has a force of 0.3 N each, the 4th isunknown. The moment of inertia has a constant value of I =0.001 kg*m^2 The torque acting on the square platform is = I * w or = 0.001 * 31 = 0.031 N.m Similarly,the torque acting on the square platform is = F1* a + F2* (2a) +F3* a + F4* (2a) or F4= ( - (F1* a + F2*(2a) + F3* a))/2a) or F4= (0.031 - (0.3 * 0.10 + 0.3 * 1.414 * 0.10 +0.3 * 0.10))/(1.414 * 0.10)) or F4= 0.5 N Therefore,the magnitude of the force on the 4thtube is F4= 0.5 N.

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