Domanda del libro di testo
An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25 incline. It rolls, without slipping, to the bottom. What fraction of its kinetic energy is rotational?
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Ch 12: Rotation of a Rigid Body
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 12, Problema 33c
A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. What is the speed of a point at the bottom edge of the tire?
Guida verificata passo dopo passo1
Step 1: Understand the problem. The speed of a point at the bottom edge of the tire is influenced by both the translational motion of the car and the rotational motion of the tire. At the bottom edge, the rotational velocity of the tire opposes the translational velocity of the car.
Step 2: Recall the relationship between linear velocity and angular velocity. The linear velocity of a point on the edge of a rotating object is given by the formula: , where is the radius of the tire and is the angular velocity.
Step 3: Calculate the radius of the tire. The diameter is given as 60 cm, so the radius is half of that: cm or m.
Step 4: Determine the angular velocity of the tire. The car's translational speed is related to the tire's angular velocity by the formula: . Rearrange to solve for : . Substitute m/s and m to find .
Step 5: Combine the translational and rotational velocities. At the bottom edge of the tire, the rotational velocity opposes the translational velocity. The total speed of the point at the bottom edge is given by: . Substitute the values to find the result.
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Linear Speed
Linear speed refers to the distance traveled per unit of time by an object moving along a path. In this context, the car's speed of 20 m/s indicates how fast the entire vehicle is moving forward. Understanding linear speed is crucial for analyzing the motion of points on the tire, as it helps relate the speed of the car to the rotational motion of the tire.
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Percorso guidato
07:31
Linear Thermal Expansion
Rotational Motion
Rotational motion describes the movement of an object around a central axis. For a tire, this involves the rotation about its center as it rolls. The relationship between linear speed and rotational speed is essential for determining how fast a point on the tire's edge moves, as the tire's rotation affects the speed of points on its circumference.
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Percorso guidato
07:18Equations of Rotational Motion
Point of Contact Speed
The speed of a point at the bottom edge of the tire, also known as the point of contact, is influenced by both the linear speed of the car and the rotational motion of the tire. When the tire rolls without slipping, the point of contact momentarily has a speed of zero relative to the ground. Thus, to find the speed of this point, one must consider the combination of the tire's rotation and the car's forward motion.
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03:15Speeds at points on a wheel
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Domanda del libro di testo
A car tire is 60 cm in diameter. The car is traveling at a speed of 20 m/s. What is the speed of a point at the top edge of the tire?
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