The engine is mounted to the wheel at an angle ? = 20 degrees from a line tangen

Question

The engine is mounted to the wheel at an angle ? = 20 degrees from a line tangent to the edge of the wheel as shown. You find that when you light the rocket, the wheel will spin a total of 3.75 revolutions in a time 2.3 seconds while the rocket is still burning. What is the force (thrust) of the rocket, assuming the thrust is constant while it is burning?

The spinning wheel has a mass of 2.3 kg and a radius of 0.45 m, is a uniform disk, and the mass of the rocket can be neglected. Give you answer in Newtons to at least three significant digits. You won't be graded on the number of digits you provide, this is just to be sure you don't get points deducted due to rounding errors.

Explanation / Answer

here,

time, t = 2.3 s
angular speed, w = 3.75 rev = 23.75*2*pi = 149.226 rad

Moment if inertia, I
I = 0.5 * m *r^2 ( m is mass, r is radius)
I = 0.5 * 2.3 * 0.45^2
I = 0.233 Kg.m^2

torque, t = I * alpha ( I is moment of inertia, alpha = angular speed)

also translational torque, t = F*r*Cos20 ( F is force)

Therefore, F*r*Cos20 = I*w^2*r (alpha = w^2*r)

Solvign for Thrust force,
F = I*w^2/(Cos20)
F = 0.233 * 149.226^2/Cos20
F = 5521.526 N

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