A thin, square plate of side 0.40 m and mass 4.0 kg lies in the xy-plane and is free to rotate about a perpendicular axle through its center. Two horizontal forces act in the plane of the plate for a brief interval Δt:
• Force F1 = 12 N acts at the midpoint of the right edge, directed upward (along +y).
• Force F2 = 8.0 N acts at the upper-left corner, directed to the right (along +x).
Neglect any forces other than F1 and F2.
(a) Compute the torque due to each force about the plate’s center. Indicate magnitude and direction (clockwise or counter-clockwise).
(b) Determine the net torque on the plate and hence its angular acceleration during the interval Δt. The moment of inertia of the square plate about its center is 61ML2.
(c) The forces act for Δt=0.20s. Assuming the plate is initially at rest, calculate its angular velocity immediately after the interval concludes.
(d) Discuss whether the center of mass of the plate experiences any translational acceleration during Δt. Support your answer by analyzing the vector sum of forces.