Question

1. Consider a uniform rectangular plate with mass M, side lengths a and 2a, and negligible thickness. In the following, ignore gravitational and frictional forces. a. Identify the principal axes and derive the principal moments of inertia 2a b. The plate is made to rotate with a constant angular velocity around an axis coincident with a diagonal of the rectangle as shown. Express the angular momentum vector in terms of the body coordinate system consisting of the body's principal axes What external torque is required to keep the plate rotating as described in part (b)? c

Answer 1

Principal are always pass through the Centre of mass. a Now we have to calculate the of centre of mass. position x Corigin) m, 4mm , mmmz ama mot my la Amza 4 mnim ton 4 am Mymy mmmz+my 0+ mxot my at mya um 2am um - - Principal anes is the anis the point (a, a) a possing through

- I - Intly Мама - I - 51a² We know vedor T aoogle angular momentum ryp Iw Now we have to calculate moment of inertia about its diagonal I 228 mnentotinertia of the trangular plate - 2x(+6 (M), 2) - 12m x 4ar 2oxa Maz V (a) a 2 2 292 √4a²tan

:12 - Ęg mata c. Now, torque 22 IL Tea Zema? W