 Ch 5. Rigid Body General Motion Multimedia Engineering Dynamics Fixed Axis Rotation Plane Motion Velocities Zero Velocity Point Plane Motion Accelerations Multiple Gears Rot. Coord. Velocities Rot. Coord. Acceleration
 Chapter - Particle - 1. General Motion 2. Force & Accel. 3. Energy 4. Momentum - Rigid Body - 5. General Motion 6. Force & Accel. 7. Energy 8. Momentum 9. 3-D Motion 10. Vibrations Appendix Basic Math Units Basic Equations Sections Search eBooks Dynamics Fluids Math Mechanics Statics Thermodynamics Author(s): Kurt Gramoll ©Kurt Gramoll STATICS - THEORY Rotating Point Velocity of Gear Edge Tangential Points on Two Rotating Gears Gears are common in mechanical equipment and are used to transfer load and to change velocities. First, consider a point on a circular rotating body. The body rotates by dθ over time dt. The change in displacement is      dr = r dθ By dividing by dt, the velocity of the point is      dr/dt = r dθ/dt This can be written in vector form as      v = ω × r The velocity direction is tangent to the circular path of point P. Since the velocity is always tangential to the radius, two touching objects will have identical velocities at the point of contact. Similarly, tangent accelerations are equal, but the normal accelerations are not.

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