Domanda del libro di testo
A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?
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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 9
What is the rotational kinetic energy of the earth? Assume the earth is a uniform sphere. Data for the earth can be found inside the back cover of the book.
Guida verificata passo dopo passo1
Start by recalling the formula for rotational kinetic energy: , where is the moment of inertia and is the angular velocity.
For a uniform sphere, the moment of inertia is given by , where is the mass of the sphere (Earth) and is its radius.
Substitute the mass and radius of the Earth into the moment of inertia formula. The mass of the Earth is approximately kg, and the radius is approximately m.
Determine the angular velocity of the Earth. The Earth completes one rotation in approximately 24 hours. Convert this period into seconds and use the formula , where is the period of rotation.
Finally, substitute the values of and into the rotational kinetic energy formula to calculate the result.
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Rotational Kinetic Energy
Rotational kinetic energy is the energy an object possesses due to its rotation. It is calculated using the formula KE_rot = 1/2 I ω², where I is the moment of inertia and ω is the angular velocity. For a uniform sphere, the moment of inertia can be determined using I = 2/5 m r², where m is the mass and r is the radius of the sphere.
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Percorso guidato
06:07
Intro to Rotational Kinetic Energy
Moment of Inertia
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. For a uniform sphere, the moment of inertia is given by I = 2/5 m r², which reflects how the mass is distributed throughout the sphere, affecting its rotational dynamics.
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11:47Intro to Moment of Inertia
Angular Velocity
Angular velocity is a vector quantity that represents the rate of rotation of an object around an axis. It is typically measured in radians per second. For the Earth, angular velocity can be calculated based on its rotation period, which is approximately 24 hours for a complete rotation, allowing us to determine how quickly it spins on its axis.
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06:18Intro to Angular Momentum
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