Derivation of equation of motion
[DOC File]A Brief Synopsis of Kane’s Method and a few Applications
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Integration of the equation of motion to give the Bernoulli equation actually corresponds to the work-energy principle often used in the study of dynamics. With certain assumptions, a statement of the work-energy principle may be written as follows: The work done on a particle by all forces acting on the particle is equal to the change of the ...
[DOC File]Chapter 5 Pressure Variation in Flowing Fluids
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(10 points) Show that the particle executes simple harmonic motion and calculate the period of the motion (Ignore any effects of rotation). (a) The derivation of the force is identical to that in Section 6.2 except here r < R. This means that in the last integral equation, (6.2.7), the limits on u are R – r to R + r. (b) , …
[DOC File]Motion and Forces - UCLA Physics & Astronomy
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Newton's laws predict the motion of most objects. As a basis for understanding this concept: ... In Standards 1g and 1l* the expression for centripetal force and centripetal acceleration are given without derivation. ... the equation aC = VT2/r where aC is the centripetal acceleration and …
[DOC File]EXERCISE 2-1
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Motion of a rocket. Force on rectangular sluice gate. Water hammer. 6.3 Moment of Momentum Equation 6.1 Derivation of the Basic Equation. Recall RTT: VR=velocity relative to CS=V – VS=absolute – velocity CS. Subscript not shown in text but implied! i.e., referenced to CV.
[DOC File]Force and Motion 2
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b) Show how the equation of motion is simplified by replacing the stress components with the appropriate gradients in the displacement components to derive Navier’s equations of motion. Expand and use the third equation of motion in component form to illustrate the steps of the derivation. The equation of motion contains derivatives of the ...
[DOC File]Motion and Forces - UCLA Physics & Astronomy
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Work out the theory in the space below. Draw free-body diagrams and set up Newton’s equation of motion for each body. Derive the theoretical equation that gives the acceleration a of the system as a function of the system parameters: mL , mB , mH , ( , and g.
Derivation of Equations of Motion - Algebraic, Graphical ...
Equation (3) will be of use for deriving how the equation of motion is modifying for objects in a rotating coordinates system. 2. Equations of motion in a rotating frame. Consider an orthogonal coordinate system which is rotating about an arbitrary axis with constant angular velocity as seen in figure 3.
[DOC File]Chapter 9: Equations of motion in a rotating frame and ...
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the equation aC = VT2/r where aC is the centripetal acceleration and VT is the tangential speed. It is also easy to show that the units of this equation are correct. Finally, since F = ma, it naturally follows that centripetal force FC = maC= m(vT)2/r.
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