Lesson 6-3 The Scalar Product AP Physics C. 6 – 3 The scalar product, or dot product, is a mathematical operation used to determine the component of a.

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Lesson 6-3 The Scalar Product AP Physics C

6 – 3 The scalar product, or dot product, is a mathematical operation used to determine the component of a given force in the direction of the displacement. It involves multiplying one vector by a second vector to produce a scalar. This is a combination of two vectors and the cosine of the angle between their directions. The scalar product can be either A times the component of in the direction of, or B times the component of in the direction of.

Properties of Scalar Products __If __________________Then____________________ Either Furthermore, Because is parallel to itself Commutative rule of multiplication Distributive rule of multiplication

The rule for differentiating a dot product (scalar product) is

p 184 Practice 6-6

Work in scalar-product notation Definition of work

Power – the rate at which a force does work, or the rate of transfer of energy Power is a scalar quantity like work and energy. The SI unit of power is the watt (W). In the US customary system, the unit of power is the foot-pound per second. A horsepower (hp) is a common multiple of this unit. A unit of energy, not power, is the kilowatt-hour (kW∙h).

p 187 Practice 6-8

HW p 198 # 37 – 42, 47, 48 – 50