A uniform square metal plate of side length and mass is pivoted at one corner about…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A uniform square metal plate of side length 0.40m and mass 3.0kg is pivoted at one corner about an axis perpendicular to its plane and passing through that corner. The plate is initially at rest.
Two identical forces of magnitude 12N act continuously:
• Force F1 is applied at the midpoint of one edge containing the pivoted corner.
• Force F2 is applied at the midpoint of the edge adjacent to the first edge (so the forces act along edges that meet at the pivoted corner). The directions of the forces are such that they produce a net torque tending to rotate the plate counter-clockwise about the pivot.
Ignore any frictional torque at the pivot.
(a) Derive an expression for the rotational inertia of the square plate about the pivot using appropriate theorems. Then calculate its numerical value.
(b) For each force, determine the magnitude of the torque about the pivot and state its direction. Explain how you obtained the lever arm in each case.
(c) Compute the net torque acting on the plate and hence determine the angular acceleration produced.
(d) At the instant when the plate has rotated through a small angle so that the midpoint of the edge opposite the pivot is instantaneously moving horizontally, calculate the magnitude of the linear acceleration of that midpoint.