Perpetual Physics Lectures [SK]

Perpetual Physics Lectures [SK] - General Physics I...

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Some material taken from: Halliday, Resnick, and Krane. Physics Kinematics - the branch of mechanics concerned with motion without reference to its cause (mass or force) Distance (scalar) vs. Displacement (vector) ` Same SI units: length/time = m/s ± Average Speed = Distance/ Δ t ± v = v avg at the midpoint of the time interval ( Δ t/2) when the acceleration is constant Average Velocity = Displacement/ Δ t ± Instantaneous Velocity = dx/dt ± Speed (scalar) vs. Velocity (vector) ` Same SI units: length/time 2 = m/s 2 ± Average acceleration = Δ v/ Δ t ± Instantaneous acceleration = dv/dt = [d 2 /dt 2 ]x ± NOTE: naught = initial (t=0) value of variable (Does not contain "x") v = v o + at (Does not contain "v") x = x o + v o t + (1/2)at 2 (Does not contain "t") v 2 = v o 2 + 2a(x - x o ) (Does not contain "a") x = x o + (1/2)(v o + v)t (Does not contain "v o ") x = x o + vt + (1/2)at 2 Equations for Motion with Constant Acceleration ± Acceleration ` Constant acceleration; | a | = | g | (the acceleration due to Earth's gravity) = 9.8 m/s 2 = 32.2 ft/s 2 ± Free-fall motion ` Motion in One Dimension Scalars - quantity fully described by a magnitude alone ` Vector - quantity fully described by both a magnitude and direction ` A vector has no origin; can be displaced anywhere in coordinate system and contains same information ± In 2-D, the vector is the hypotenuse of the triangle drawn with the vector components as legs In 2-D, a x = | a |Cos θ ; a y = | a |Sin θ ; θ = angle between vector and x-axis Euclidean geometry applies: angles of triangles determined by vector components! A vector can be interpreted as the hypotenuse of the geometric figure that its component vectors form ± A vector has a component for each unit vector defining the basis of the vector space ± Vectors are a convenient way to solve a system of equations: each coordinate direction represents a single independent problem ± Two vectors are equal if and only if all of their components are equal ± Vector addition: add respective components of each vector; associative and commutative ± Scalar-Vector product results in multiplying each component of vector by the scalar If two vectors are perpendicular, scalar product = 0 If two vectors are parallel, the magnitude is maximized (= | a || b |) Scalar/Inner/Dot product of two vectors yields a scalar; represents their degree of overlap or projection of one onto another; | a · b | = | a || b |Cos θ Vector/Cross product of two vectors yields a vector; represents "sense" of the Vector products ± Vector Addition/Resolution ` Scalars vs. Vectors General Physics I Conceptual Overview Saturday, February 25, 2006 4:36 PM Perpetual Gen Physics Lectures Page 1
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Right-hand rule applies to direction of resultant vector If two vectors are parallel, vector product = 0 If two vectors are perpendicular, magnitude of vector product is maximized
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Perpetual Physics Lectures [SK] - General Physics I...

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