Question

please help!!! detailed explanation / steps

1. The structure shown here is made from six pieces attached as shown. Each piece has the same mass, M. The pieces are as follows: One solid, uniform disk with diameter D. Four identical thin uniform rods of length D, connected to the disk as showrn (opposing pairs of rods aligned with the disk center). One thin, uniform ring connected to the outer ends of the four rods, as shown. The entire structure is laid flat, at rest, on a frictionless surface and pinned to the surface with a frictionless pin at Point P. (So the diagram is an overhead view.) rod ring rod disk rod Point P is located at the midpoint of one of the rods, as shown. Point X is located on the edge of the disk-directly opposite to point P-as shown. rod Then at time t 0, a steady torque, t, is applied to the structure around point P, and as a result, the structure begins to rotate around that pin. a. Find an algebraic expression for a (), the magnitude of the acceleration of point X, as a function of time, t b. Find an algebraic expression for W(t), the total work done on the structure, as a function of time, t. Each expression may contain only known values (and the variable t). These are known values: M, D, T.

Answer 1

The structure shown has six pieces and having the same mass M. The first one is the uniform solid disk with diameter D, four thin uniform identical rods and one thin uniform ring connected to the outer ends of the four rods The acceleration has tangential and the centripetal components The tangential component of the acceleration is, 3d The centripetal component of the acceleration is, And The magnitude of the acceleration is,

3d 3d I.

The total work done on the one structure is Tt 2I The moment of inertia about the centre of mass is, M D com22 MD2 12 3D 12 161 24

From the parallel axis theorem, 24 305 m 24