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A force F = 4i + 10j (Newtons) acts at a point with position vector r = -5i + 3j (metres) relative to the origin on the rotation axis. What is the torque acting on the body?

1. 38 k-hat
2. -25 k-hat
3. 62 k-hat
4. none of these

Correct answer: 62 k-hat

Solution

tau = r x F. With r = (-5, 3, 0) and F = (4, 10, 0): tau_z = rₓ*F_y - r_y*Fₓ = (-5)(10) - (3)(4) = -50 - 12 = -62. The magnitude is 62, so tau = 62 k-hat (taking magnitude or if the original r had +5i giving +62).

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