Question

A uniform block of mass m, of depth a, of width 2a and of height 3a is rotated along an axis passing through its diagonal at an angular velocity w. Using a coordinate system whose origin is at the center of the block:

a) Determine the kinetic energy of the block.

b)Find the angle that exists between the angular velocity vector and the original angular momentum vector.

Answer 1

Solution:

1.

As we know the kinetic energy of the block can be given as:

K = 1/2 I w²

=> K = 1/2 (m/3 (a²+4a²))w²

=> K = 5/6 ma²w²

2.

As we know;

The direction of angular velocity and angular momentum are perpendicular to the plane of rotation. Using the right-hand rule,

the direction of both angular velocity and angular momentum is defined as the direction in which the thumb of your right-hand

points when you curl your fingers in the direction of rotation.