1 Physics And Measurement 2 Motion In One Dimension 3 Vectors 4 Motion In Two Dimensions 5 The Laws Of Motion 6 Circular Motion And Other Applications Of Newton’s Laws 7 Energy Of A System 8 Conservation Of Energy 9 Linear Momentum And Collisions 10 Rotation Of A Rigid Object About A Fixed Axis 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Universal Gravitation 14 Fluid Mechanics 15 Oscillatory Motion 16 Wave Motion 17 Sound Waves 18 Superposition And Standing Waves 19 Temperature 20 The First Law Of Thermodynamics 21 The Kinetic Theory Of Gases 22 Heat Engines, Entropy, And The Second Law Of Thermodynamics 23 Electric Fields 24 Gauss’s Law 25 Electric Potential 26 Capacitance And Dielectrics 27 Current And Resistance 28 Direct-current Circuits 29 Magnetic Fields 30 Sources Of The Magnetic Field 31 Faraday’s Law 32 Inductance 33 Alternating Current Circuits 34 Electromagnetic Waves 35 The Nature Of Light And The Principles Of Ray Optics 36 Image Formation 37 Wave Optics 38 Diffraction Patterns And Polarization 39 Relativity Chapter3: Vectors
Chapter Questions Section: Chapter Questions
Problem 3.1QQ: Which of the following are vector quantities and which are scalar quantities? (a) your age (b)... Problem 3.2QQ: The magnitudes of two vectors A and B are A = 12 units and B = 8 units. Which pair of numbers... Problem 3.3QQ: If vector B is added to vector A, which two of the following choices must be true for the resultant... Problem 3.4QQ: Choose the correct response to make the sentence true: A component of a vector is (a) always, (b)... Problem 3.5QQ: For which of the following vectors is the magnitude of the vector equal to one of the components of... Problem 3.1OQ: What is the magnitude of the vector (10i 10k) m/s? (a) 0 (b) 10 m/s (c) 10 m/s (d) 10 (e) 14.1 m/s Problem 3.2OQ: A vector lying in the xy plane has components of opposite sign. The vector must lie in which... Problem 3.3OQ: Figure OQ3.3 shows two vectors D 1, and D2. Which of the possibilities (a) through (d) is the vector... Problem 3.4OQ: The culling tool on a lathe is given two displacements, one of magnitude 4 cm and one of magnitude 3... Problem 3.5OQ: The magnitude of vector A is 8 km, and the magnitude of B is 6 km. Which of the following are... Problem 3.6OQ: Let vector point from the origin into the second quadrant of the xy plane and vector point from the... Problem 3.7OQ: Yes or no: Is each of the following quantities a vector? (a) force (b) temperature (c) the volume of... Problem 3.8OQ: What is the y component of the vector (3i 8k) m/s? (a) 3 m/s (b) 8 m/s (c) 0 (d) 8 m/s (e) none of... Problem 3.9OQ: What is the x component of the vector shown in Figure OQ3.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e)... Problem 3.10OQ: What is the y component of the vector shown in Figure OQ3.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e)... Problem 3.11OQ: Vector lies in the xy plane. Both of its components will be negative if it points from the origin... Problem 3.12OQ: A submarine dives from the water surface at an angle of 30 below the horizontal, following a... Problem 3.13OQ: A vector points from the origin into the second quadrant of the xy plane. What can you conclude... Problem 3.1CQ: Is it possible to add a vector quantity to a scalar quantity? Explain. Problem 3.2CQ: Can the magnitude of a vector have a negative value? Explain. Problem 3.3CQ Problem 3.4CQ Problem 3.5CQ Problem 3.1P: The polar coordinates of a point are r = 5.50 in and = 240. What are the Cartesian coordinates of... Problem 3.2P: The rectangular coordinates of a point are given by (2, y). and its polar coordinates are (r, 30).... Problem 3.3P: Two points in the xy plane have Cartesian coordinates (2.00, 4.00) m and (3.00, 3.00) m. Determine... Problem 3.4P Problem 3.5P: The polar coordinates of a certain point are (r = 4.30 cm, = 214). (a) Find its Cartesian... Problem 3.6P: Let the polar coordinates of the point (x, y) be (r, ). Determine the polar coordinates for the... Problem 3.7P: A surveyor measures the distance across a straight river by the following method (Fig. P3.7).... Problem 3.8P: Vector A has a magnitude of 29 units and points in the positive y direction. When vector B is added... Problem 3.9P: Why is the following situation impossible? A skater glides along a circular path. She defines a... Problem 3.10P: A force F1 of magnitude 6.00 units acts on an object at the origin in a direction = 30.0 above the... Problem 3.11P: The displacement vectors A and B shown in Figure P3.9 both have magnitudes of 3.00 m. The direction... Problem 3.12P: Three displacements are A=200m due south, B=250m due west, and C=150m at 30.0 east of north. (a)... Problem 3.13P: A roller-coaster car moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 above the... Problem 3.14P: A plane flies from base camp to Lake A, 280 km away in the direction 20.0 north of east. After... Problem 3.15P: A vector has an x component of 25.0 units and a y component of 40.0 units. Find the magnitude and... Problem 3.16P: Vector has a magnitude of 35.0 units and points in the direction 325 counterclockwise from the... Problem 3.17P: A minivan travels straight north in the right lane of a divided highway at 28.0 m/s. A camper passes... Problem 3.18P: A person walks 25.0 north of east for 3.10 km. How far would she have to walk due north and due east... Problem 3.19P: Obtain expressions in component from for the position vectors having the polar coordinates (a) 12.8... Problem 3.20P: A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and... Problem 3.21P: While exploring a cave, a spelunker starts at the entrance and moves the following distances in a... Problem 3.22P: Use the component method to add the vectors A and B shown in Figure P3.9. Both vectors have... Problem 3.23P Problem 3.24P: A map suggests that Atlanta is 730 miles in a direction of 5.00 north of cast from Dallas. The same... Problem 3.25P: Your dog is running around the grass in your back yard. He undergoes successive displacements 3.50 m... Problem 3.26P: Given the vectors A=2.00i+6.00j and B=3.00i2.00j, (a) draw the vector sum C=A+B and the vector... Problem 3.27P: A novice golfer oil the green takes three strokes to sink the ball. The successive displacements of... Problem 3.28P: A snow-covered ski slope makes an angle of 35.0 with the horizontal. When a ski jumper plummets onto... Problem 3.29P: The helicopter view in Fig. P3.15 shows two people pulling on a stubborn mule. The person on the... Problem 3.30P: In a game of American football. a quarterback takes the ball from the line of scrimmage. runs... Problem 3.31P: Consider the three displacement vectors m, m, and m. Use the component method to determine (a)... Problem 3.32P: Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector R has x and y... Problem 3.33P Problem 3.34P Problem 3.35P: Vector A has a negative x component 3.00 units in length and a positive y component 2.00 units in... Problem 3.36P: Given the displacement vectors A=(3i4j+4k)m and B=(2i+3j7k)m, find the magnitudes of the following... Problem 3.37P Problem 3.38P: Three displacement vectors of a croquet ball are shown in Figure P3.22, where A=20.0 units, B=40.0... Problem 3.39P: A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude... Problem 3.40P: Figure P3.28 illustrates typical proportions of male (m) and female (f) anatomies. The displacements... Problem 3.41P: Express in unit-vector notation the following vectors, each of which has magnitude 17.0 cm. (a)... Problem 3.42P: A radar station locates a sinking ship at range 17.3 kin and bearing 136 clockwise from north. From... Problem 3.43P: Review. As it passes over Grand Bahama Island, the eye of a hurricane is moving in a direction 60.0... Problem 3.44P: Why is the following situation impossible? A shopper pushing a cart through a market follows... Problem 3.45P: Review. You are standing on the ground at the origin of a coordinate system. An airplane flies over... Problem 3.46P: In Figure P3.33, the line segment represents a path from the point with position vector (5i+3j)m to... Problem 3.47P: In an assembly operation illustrated in Figure P3.30. a robot moves an object first straight upward... Problem 3.48AP: A fly lands on one wall of a room. The lower-left corner of the wall is selected as the origin of a... Problem 3.49AP: As she picks up her riders, a bus driver traverses four successive displacements represented by the... Problem 3.50AP: A jet airliner, moving initially at 300 mi/h to the east, suddenly enters a region where the wind is... Problem 3.51AP: A person going for a walk follows the path shown in Figure P3.35. The total trip consists of four... Problem 3.52AP: Find the horizontal and vertical components of the 100-m displacement of a superhero who flies from... Problem 3.53AP: Review. The biggest stuffed animal in the world is a snake 420 m long, constructed by Norwegian... Problem 3.54AP: An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 800 m,... Problem 3.55AP: In Figure P3.55, a spider is resting after starting to spin its web. The gravitational force on the... Problem 3.56AP: The rectangle shown in Figure P3.56 has sides parallel to the x and y axes. The position vectors of... Problem 3.57AP: A vector is given by R=2i+j+3k. Find (a) the magnitudes of the x, y, and z components; (b) the... Problem 3.58AP: A ferry transports tourists between three islands. It sails from the first island to the second... Problem 3.59AP: Two vectors A and B have precisely equal magnitudes. For the magnitude of A+B to be 100 times larger... Problem 3.60AP: Two vectors A and B have precisely equal magnitudes. For the magnitude of A+B to be larger than the... Problem 3.61AP: Lei A = 60.0 cm at 270 measured from the horizontal. Let B = 80.0 cm at some angle . (a) Find the... Problem 3.62AP: After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of... Problem 3.63AP: Review. The instantaneous position of an object is specified by its position vector leading from a... Problem 3.64AP: Ecotourists use their global positioning system indicator to determine their location inside a... Problem 3.65AP: A rectangular parallelepiped has dimensions a, b, and c as shown in Figure P3.45. (a) Obtain a... Problem 3.66AP: Vectors A and B have equal magnitudes of 5.00. The sum of A and B is the vector 6.00j. Determine the... Problem 3.67CP: A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0... Problem 3.61AP: Lei A = 60.0 cm at 270 measured from the horizontal. Let B = 80.0 cm at some angle . (a) Find the...
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Concept explainers
What's the average angular acceleration of a maximum-duration CD during its 74-min playing time? Take the direction of rotation of the disc to be positive
Transcribed Image Text: A compact disc (CD) stores music in a coded pattern
of tiny pits 10 m deep. The pits are arranged in a
track that spirals outward toward the rim of the disc,
the inner and outer radii of this spiral are 25.0 mm
-7
and 58.0 mm, respectively As the disc spins inside a
CD player, the track is scanned at a constant linear
speed of 1.25 m/s.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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