A pendulum is made of two discs, one with mass M and radius R and the other with mass 2M and radius R, which are separated by a massless rod. The lighter disc is pivoted through its centre by a small pin. The discs lie on the same plane and their centres are a distance L apart. Find the period for small oscillations.
3 answers
A uniform lamina consists of a disc with radius R with a disc of radius r cut off from its centre, with r < R. The total mass of the object is M. Find the moment of inertia when the lamina rotates about an axis perpendicular to the lamina, thought its centre.
An object consists of two thin rods, AB with mass M and length 2L, and CD, of mass 2M and length L, joined together at right angles at their midpoints to form a cross. Let E be the point where the two rods intersect. Find the moment of inertia of the object when it rotates about the following axes of rotation:
(a) An axis along rod AB.
(b) An axis along rod CD.
(c) An axis through point E, perpendicular to the cross.
(d) An axis through point A, perpendicular to the cross.
(a) An axis along rod AB.
(b) An axis along rod CD.
(c) An axis through point E, perpendicular to the cross.
(d) An axis through point A, perpendicular to the cross.
Find the moment of inertia of an A × A × A cube with mass M, for the following axes of rotation:
(a) An axis through the midpoints of two opposing sides.
(b) An axis along one of the edges of the cube.
(a) An axis through the midpoints of two opposing sides.
(b) An axis along one of the edges of the cube.
1 answer