Question

A pinning object has intial momentum, L1= 2i+5j+7k. three seconds later, the angular momentum is L2= 3i+4j+10k. what is the magnitude and direction of the average torque required to cause this change? assuming that the object is a rectangular plate with the sides of lengtg 2 and 3 meters and mass 20kg spinning about the center of symmetry with the axis parallel to the torque vector, what is the angular acceleration of the object?

Answer 1

Let thed torque applied tot he body be T
then T = (change in angular momentum)/time
T = (L2 - L1)/t = (3i + 4j + 10k - 2i -5j - 7k)/3 = (i - j + 3k)/3 = 0.33i - 0.33j + k

Now, angular acceleration = alpha
and moment of inertia = I
then I*alpha = T
but I for rectangular plate about an acis passing through centre of mass perpendiculr to the rectangular plate , I = m(h^2 + w^2)/12
so, 20(2^2 + 3^2)*alpha /12 = 0.33i - 0.33j + k
alpha = 0.01536 i - 0.015369j + 0.046107 k