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What is the magnitude of force F?

Torque = FRsinβ

Torque = I∂

∂ = ωf - ωi / t

ωf = 2∏f = 383.9026 rad/s

ωf = θ/t; 609 rad / 383.9026 rad/s = 1.586, so t = 1.586 s

∂ = 383.9026 / 1.586 = 242.005 rad/s^2

Torque = (1/2)(MR^2)(∂)

Torque = (1/2)(3.13)(.193)^2(242.005) = 14.1076

14.1076 = F(.193)(sin 45.8)

F = 102 N

But 102 N is wrong so I guess Torque really does not = FRsinβ

Can anyone help here....cause I have no clue why or how this could be wrong...