mechanika
9

MECHANICS II, exam 2, 24 June 2010

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Studenfs given name, surname, and number of the group Elżbieta Jarzębowska (13), Wiesław Łucjanek (14)

1	2	3	Tut.	Z

Problem 1. A planetary gear consists of a main wheel of radius c, a connecting rod and a satellite wheel of radius b. The satellite wheel may roli on the main wheel without slipping. The main wheel and the connecting rod rotate with absolute angular velocities eąual to (Oq and a>_k, respectively. The sense of each velocity is indicated in the figurę. Determine the absolute angular velocity co_s of the satellite wheel.

Problem 2. A system of two bodies, i.e. a thin uniform rod of mass m and length L and a disk of mass M and radius b, may move in the piane x-y.

The absolute angular velocity of the rod is eąual to Q, and the relative angular velocity of the disk with respect to the rod is eąual to a^. Both angular velocities are constants. Determine the linear momentum, the angular momentum with respect to the origin O, and the kinetic energy of the system

at its position indicated in the figurę. Use the--------

reference frame ffom the figurę to present the finał results.

Problem 3. A system is composed of a rectangular piąte of mass m and a particie of mass M fixed on a weightless bracket of length L. It may rotate about the vertical axis fixed at bearings A and B with an angular veIocity co = const. Determine the reaction in the bearing A. Neglect the system weight. Moments of inertia of a rectangular piąte are:

/, = —Ma² I = —Mb² I =—M(a² +b²)

¹ 12 ^y 12 ^z 12 '