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Mastering Physics with Vectors and Trigonometry

Learn how to solve physics problems using vectors and trigonometry principles. Understand scalar and vector quantities, vector addition and components. Practice adding vectors by sketching and analyzing components. Master the role of units in problem-solving with examples.

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Mastering Physics with Vectors and Trigonometry

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  1. Chapter one Role of units in problem solving Trigonometry Scalars and Vectors Vector Addition and Subtraction Addition of Vectors by Components

  2. Role of Units in Problem Solving • SI units for mass, length, and time are the kilogram, meter, and second. • Only SI units, base and derived, are used on the AP Physics B exam. • *You will often need to be able to determine the validity of equations by analyzing the dimensions of the quantities involved. • Example: Pg. 21, #7

  3. Trigonometry • Trigonometry is the study of triangles, often right triangles. • Lengths of the sides of a right triangle can be used to define some useful relationships called sine, cosine, and tangent. • The trig relationships will be particularly helpful when dealing with vectors. • Example: pg. 21, #11

  4. Scalars and Vectors • A scalar is a quantity which has no direction associated with it, only magnitude: mass, volume, time, temp, distance, speed, work, energy. • A vector is a quantity which has both magnitude (size) and direction (angle): displacement, velocity, acceleration, force, weight, momentum. • We can graphically add vectors to each other by placing the tail of one vector onto the tip of the previous vector. • Example: #4- white board • Example: pg 22, #23

  5. Vector Addition Cont. • Resultant vector- displacement from the origin to the tip of the last vector, it is equal to the vector sum of the individual vectors • Adding displacement vectors in any order will achieve the same resultant. Thus, the addition of vectors is commutative. • Equilibrant vector- can cancel or balance the resultant vector, it is equal in magnitude and opposite in direction of the resultant vector. • Example: pg 22, #25

  6. Components of a Vector • We may work with vectors mathematically by breaking them into their components. Vector A can have the x-axis component Ax and its y-axis component Ay. (white board sketch) • We can use trigonometry to find the magnitudes of these different components. • Example: pg 23, # 33

  7. Vector Addition by Components • Earlier we added vectors together graphically. We can also use the components to find the resultant of any number of vectors. • Example: Add A+B+C • A= 4 meters at 30 degrees from the x-axis (NE) • B = 3 meters at 45 degrees from the x-axis (NE) • C = 5 meters at 25 degrees from the y- axis (in the south/west direction) • The properties of vectors can be applied to any vector. • Example: pg 23, #41 • Time permitting: pg 23, #65

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