Mechanical engineering handbook by Kreith F.

By Kreith F.

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Example text

F = µsN is valid. To determine the unknowns: 1. Construct the free-body diagram. 2. Write F = µsN for all surfaces where motion is impending. 3. Determine µs or the required forces from the equation of equilibrium. Bodies, forces, coefficients of friction are known. Impending motion is specified, but the exact motion is not given. The possible motions may be sliding, tipping or rolling, or relative motion if two or more bodies are involved. Alternatively, the forces or coefficients of friction may have to be determined to produce a particular motion from several possible motions.

When using normal and tangential components, it is common to forget to include the component of normal acceleration, especially if the particle travels at a constant speed along a curved path. 5 Motion of a particle in polar coordinates. 6. 6 Motion of a particle in cylindrical coordinates. Motion of a Particle in Spherical Coordinates Spherical coordinates are useful in a few special cases but are difficult to apply to practical problems. The governing equations for them are available in many texts.

Conservation of Momentum The principle of conservation of linear and angular momentum of particles can be extended to rigid bodies that have no external forces or moments acting on them. 71) IC ω 1 = IC ω 2 For a system of rigid bodies, use the same fixed reference point O for all parts of the system. 72) There are two important points to remember when using these equations. First, ∆HC = 0 does not imply that ∆HO = 0, or vice versa. Second, conservation of momentum does not require the simultaneous conservation of both angular and linear momenta (for example, there may be an angular impulse while linear momentum is conserved).