Textbook Question
FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particle's angular velocity at t = 4s
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Ch 04: Kinematics in Two Dimensions
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 4, Problem 27
The earth's radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore takes 9.0 hours. What is the plane's angular velocity with respect to the earth's surface? Give your answer in °/h.
Verified step by step guidance1
Step 1: Understand the relationship between linear velocity and angular velocity. Angular velocity (ω) is related to linear velocity (v) by the formula: ω = v / r, where r is the radius of the circular path.
Step 2: Convert the earth's radius from miles to the same unit as the distance traveled (miles). Since the radius is already given in miles (4000 miles), no conversion is needed.
Step 3: Calculate the plane's linear velocity (v) by dividing the distance traveled (5000 miles) by the time taken (9.0 hours). Use the formula: v = distance / time.
Step 4: Substitute the values of linear velocity (v) and the earth's radius (r) into the formula for angular velocity: ω = v / r. This will give the angular velocity in radians per hour.
Step 5: Convert the angular velocity from radians per hour to degrees per hour. Use the conversion factor: 1 radian = 57.2958 degrees. Multiply the angular velocity in radians per hour by this factor to express the result in degrees per hour.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Velocity
Angular velocity is a measure of how quickly an object rotates around a specific point or axis. It is typically expressed in degrees per unit of time, such as degrees per hour. In this context, it describes how fast the plane is moving in relation to the Earth's rotation as it travels from Kampala to Singapore.
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Circumference of the Earth
The circumference of the Earth can be calculated using the formula C = 2πr, where r is the radius. Given the Earth's radius of about 4000 miles, the circumference is approximately 25,132 miles. This value is essential for understanding the relationship between linear distance traveled and the angular displacement of the Earth during the flight.
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Equatorial Motion
Equatorial motion refers to the movement of objects along the equator, where the Earth's rotational speed is highest. Since both Kampala and Singapore are near the equator, the plane's flight path can be analyzed in terms of how it relates to the Earth's rotation. This concept is crucial for calculating the angular velocity of the plane as it travels between these two points.
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Related Practice
Textbook Question
Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at 25 m/s?
Textbook Question
The radius of the earth's very nearly circular orbit around the sun is 1.5 x 1011 m. Find the magnitude of the earth's velocity.
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Textbook Question
FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?
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Textbook Question
As the earth rotates, what is the speed of a physics student in Miami, Florida, at latitude 26°. Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km.
Textbook Question
Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trent's speed relative to Susan's reference frame?
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