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Muscular Forces from Static Optimization
Muscular Forces from Static Optimization

... where m is the mass of the object, a is the linear acceleration, I, is the mass moment of inertia and α is the angular acceleration of the object. The link-segment model is broken down at the joints into segments which are treated separately as rigid bodies, creating a free-body diagram (Figure 2.2) ...
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... are told that the initial height of the dropped disk is negligible, so, we must neglect it in our considerations. That means nothing undergoes a non negligible elevation change in the process, so, gravitational potential energy is not relevant here. The new spin rate is clearly less than the origina ...
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... end of the year activity for both middle and high school physical science students. The physics of the rides is the basic material of a first-year physics course. Roller coasters demonstrate the conversion of gravitational potential into kinetic energy; rotating swing rides illustrate the vector add ...
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... Consider these two situations. On Monday morning, you leave your house and walk directly to school, 500 m from your home. On Tuesday morning, instead of walking directly to school, you take a turn off the direct route to your friend's house. From there you walk to the newsagent to buy a magazine, an ...
Realizing nonholonomic dynamics as limit of friction forces
Realizing nonholonomic dynamics as limit of friction forces

Lagrange`s Equations
Lagrange`s Equations

... of mechanics published in 1788 by the Italian-French astronomer and mathematician Lagrange (1736-1813). The Lagrangian formulation has two important advantages over the earlier Newtonian formulation. First, Lagrange's equations, unlike Newton's, take the same form in any coordinate system. Second, i ...
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Continuous Penalty Forces

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Roller Coaster (AP) Physics

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... you need it when the square of the variable for which you are solving, appears in the equation you are solving. When that is the case, carry out the algebraic steps needed to arrange the terms as they are arranged in equation 1-8 above. If this is impossible, then the quadratic formula is not to be ...
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Mass times velocity.

... illustration above. During the collision, momentum transfers from one ball to another. The law of conservation of momentum states that the combined momentum of both remains constant: One ball’s loss equals the other ball’s gain. A rifle also provides a notable example of the conservation of momentum ...
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... large sphere (large weight times small lever arm) will be equal to the clockwise torque due to the small sphere (small weight times large lever arm). Look at the figure and mentally balance the dumbbell on your finger; your finger would have to be at point a. The sun-earth system is similar to this ...
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Module P5.3 Forced vibrations and resonance

... system), period, position, potential energy, power and velocity. You should also be familiar with simple harmonic motion (see Question R2), and aware of the general features of damped harmonic motion (though this is briefly reviewed in the module). Mathematically, you will need to be familiar with e ...
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Hunting oscillation



Hunting oscillation is a self-oscillation, usually unwanted, about an equilibrium. The expression came into use in the 19th century and describes how a system ""hunts"" for equilibrium. The expression is used to describe phenomena in such diverse fields as electronics, aviation, biology, and railway engineering.
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