Vectors. Slide 2 / 36. Slide 1 / 36. Slide 3 / 36. Slide 4 / 36. Slide 5 / 36. Slide 6 / 36. Scalar versus Vector. Determining magnitude and direction

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1 Slide 1 / 3 Slide 2 / 3 Scalar versus Vector Vectors scalar has only a physical quantity such as mass, speed, and time. vector has both a magnitude and a direction associated with it, such as velocity and acceleration. vector is denoted by an arrow above the variable, Slide 3 / 3 1 Is this a vector or a scalar? Slide 4 / 3 2 Which of the following is a true statement? Time Speed Scalar Scalar It is possible to add a scalar quantity to a vector. The magnitude of a vector can be zero even though one of its components is not zero. Velocity istance isplacement Vector Scalar Vector The sum of the magnitude of two unequal vectors can be zero. Rotating a vector about an ais passing through the tip of the vector does not change the vector. Vectors must be added geometrically. Slide 5 / 3 Slide / 3 rawing Vector vector is always drawn with an arrow at the tip indicating the direction, and the length of the line determines the magnitude. etermining magnitude and direction anti-parallel Remember displacement is the distance away from your initial position, it does not account for the actual distance you moved ll of these vectors have the same magnitude, but vector runs anti-parallel therefore it is denoted negative.

2 Slide 7 / 3 Vector ddition Slide 8 / 3 Vector ddition Methods Tail to Tip Method Slide 9 / 3 Vector ddition Methods Parallelogram Method Slide 10 / 3 3 If a car under goes a displacement of 3 km North and another of to the ast what is the net displacement? Place the tails of each vector against one another. Finish drawing the parallelogram with dashed lines and draw a diagonal line from the tails to the other end of the parallelogram to find the vector sum. 5 2 km 5 km 4 7 km km Slide 11 / 3 Slide 12 / 3 4 If a car under goes a displacement of North and another of to the ast what is the total distance traveled? 5 2 km 7 km 5 km 5 Solve for θ 45 o 75 o 53 o 37 o 25 o θ

Slide 13 / 3 Vector omponents Slide 14 / 3 Multiple Vectors When dealing with multiple vectors you can just add the components in order to attain the

θ is measured starting at the ais and rotating in the direction of the y-ais.

3 Slide 13 / 3 Vector omponents Slide 14 / 3 Multiple Vectors When dealing with multiple vectors you can just add the components in order to attain the components of the vector sum. vy v v y vy θ v v y v y vector that makes an angle with the ais has both a horizontal and vertical component of velocity. θ is measured starting at the ais and rotating in the direction of the y-ais. Slide 15 / 3 Slide 1 / 3 The components of vector are given as follows: 7 The components of vectors are given as follows: and The magnitude of is closest to: Solve for the magnitude of Slide 17 / 3 Slide 18 / 3 8 The components of vector are given as follows: 9 The components of vector and are given as follows: The angle measured counter-clockwise from the -ais t vector, in degrees, is closest to: 339 o 200 o 122 o 21 o 159 o The magnitude of -, is closest to:

4 Slide 19 / 3 10 The magnitude of is 5.2. Vector lies in the 4th quadrant and forms a 30 o with the -ais. The components of and y are: Slide 20 / 3 11 The magnitude of vector is equal to vector plus vector. What is the value of vector? O y 45 O Slide 21 / 3 Slide 22 / 3 12 Vectors and are shown. Vector is given by = +. In the figure above, the magnitude of is closest to: o 30 o Slide 23 / 3 Slide 24 / 3 13 What is the magnitude of the sum of the following vectors?

Slide 25 / 3 Products of Vectors Scalar Product also known as ot Product yields a scalar quantity value can be positive, zero, or negative depending on θ. θ ranges from 0 to 180 degrees.

5 Slide 25 / 3 Products of Vectors Scalar Product also known as ot Product yields a scalar quantity value can be positive, zero, or negative depending on θ. θ ranges from 0 to 180 degrees. = = = = = = Slide 2 / 3 14 In the figure, find the scalar product of vectors and, o 4 45 o Slide 27 / 3 Slide 28 / 3 15 In the figure, find the scalar product of vectors and, o 4 45 o Products of Vectors Vector Product also known as the cross product yields another vector. = = = = - = = - = = - = Slide 29 / 3 Slide 30 / 3 1 In the figure, find the vector product of vectors and. 17 Two vectors are give as follows: o 4 45 o Solve for

6 Slide 31 / 3 18 Two vectors are give as follows: Slide 32 / 3 19 Which of the following is an accurate statement? Solve for If the vectors and are each rotated through the same angle about the same ais, the product will be unchanged. If the vectors and are each rotated through the same angle about the same ais, the product will be unchanged If a vector is rotated about an ais parallel to vector, the product will be changed. When a scalar quantity is added to a vector, the result is a vector of larger-magnitude than the original vector. Slide 33 / 3 20 Solve for the angle between vector and 21 Two vectors are given: Slide 34 / o o 57 o o o The angle between vectors and, in degrees, is: 117 o 7 o 150 o 29 o 11 o Slide 35 / 3 Slide 3 / 3 22 Two vectors are given: Solve for the magnitude of

AP Physics C - Mechanics

AP Physics C - Mechanics Slide 1 / 36 Slide 2 / 36 P Physics - Mechanics Vectors 2015-12-03 www.njctl.org Scalar Versus Vector Slide 3 / 36 scalar has only a physical quantity such as mass, speed, and time. vector has both a magnitude