By Mark D Ardema

ISBN-10: 0306486814

ISBN-13: 9780306486814

ISBN-10: 0306486822

ISBN-13: 9780306486821

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**Sample text**

The ring is given an initial angular velocity w about the vertical axis passing through the diameter containing the opening, and simultaneously the particle is released from rest (relative to the tube) at ^ = -K/2. In the subsequent motion, will the particle drop through the opening? 1 N e w t o n ' s Second Law Vector Form. '{t), as shown on Fig. 2-1. Let the resultant forces on the particles be bounded functions of the particles' positions, velocities, and time. Then Eqn. 2) If none of the forces depend explicitly on time, we say the system is autonomous.

56) Review of Newtonian Dynamics 21 where v is the speed of the center of mass and I is the moment of inertia about an axis passing through the center of mass and parallel to the axis of rotation. 57) where I A is the moment of inertia about an axis passing through a bodyfixed point that is also fixed in an inertial frame. A result that is sometimes useful is Koenig's theorem. t. an inertial frame {«, j , k}, as shown on Fig. 1-22. Introduce a frame {i',j', k'} with origin at the body's center of mass that moves in such a way that it's axes always remain parallel to those of the inertial frame (thus this frame is not body fixed).

The disk rolls on the a;y-plane without slipping, with point D remaining at the origin. Determine the kinetic energy of the disk if shaft CD rotates about the z-axis with constant angular speed n. Review of Newtonian Dynamics 4 in. 8 in. — • • Problem 1/59 1/61. Problem 1/60 A homogeneous solid right circular cone rolls on a plane without slipping. The line of contact turns at constant angular speed Q. about the 2;-axis. Find the kinetic energy of the cone. Problem 1/61 Problem 1/62 1/62. A particle of mass m slides along one radius of a circular platform of mass M.

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