Work, Energy and Power

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The scalar product A·B = |A||B|cosθ, where θ is the angle between the vectors. Geometrically, it equals the product of the magnitude of one vector and the component of the other vector along the first

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î·î = ĵ·ĵ = k̂·k̂ = 1 (dot product of a unit vector with itself equals 1) î·ĵ = ĵ·k̂ = k̂·î = 0 (dot product of perpendicular unit vectors equals zero)

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Work is defined as W = F·d = Fdcosθ, where F is force, d is displacement, and θ is angle between them. Work is zero when: (1) displacement is zero, (2) force is zero, or (3) force and displacement are

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SI unit: Joule (J). Alternative units include: erg (10⁻⁷ J), electron volt (1.6 × 10⁻¹⁹ J), calorie (4.186 J), kilowatt hour (3.6 × 10⁶ J). Dimensions: [ML²T⁻²]

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Kinetic energy is the energy possessed by a body due to its motion. K = ½mv², where m is mass and v is velocity. It's a scalar quantity and is always positive. It represents the work an object can do

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The Work-Energy Theorem states that the change in kinetic energy of a particle equals the work done on it by the net force. Mathematically: Kf - Ki = Wnet or ΔK = W, where Kf and Ki are final and init

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For a variable force, work is calculated using integration: W = ∫(xi to xf) F(x)dx. Graphically, it equals the area under the F vs x curve between xi and xf.

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Potential energy is the energy possessed by a body by virtue of its position or configuration. It's 'stored energy' that can be converted to kinetic energy when external constraints are removed. For c