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A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for rotation on its hinges?
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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 17a
A 12-cm-diameter DVD has a mass of 21 g. What is the DVD’s moment of inertia for rotation about a perpendicular axis through its center?
Guida verificata passo dopo passo1
Step 1: Identify the shape of the DVD. The DVD can be approximated as a uniform solid disk. The formula for the moment of inertia of a solid disk rotating about an axis perpendicular to its center is \( I = \frac{1}{2} m r^2 \), where \( m \) is the mass and \( r \) is the radius.
Step 2: Convert the given diameter of the DVD into its radius. The diameter is 12 cm, so the radius \( r \) is half of the diameter: \( r = \frac{12}{2} = 6 \, \text{cm} \). Convert this to meters: \( r = 0.06 \, \text{m} \).
Step 3: Convert the mass of the DVD from grams to kilograms. The mass is given as 21 g, and since \( 1 \, \text{kg} = 1000 \, \text{g} \), the mass in kilograms is \( m = \frac{21}{1000} = 0.021 \, \text{kg} \).
Step 4: Substitute the values of \( m \) and \( r \) into the formula for the moment of inertia: \( I = \frac{1}{2} m r^2 \). This becomes \( I = \frac{1}{2} \times 0.021 \times (0.06)^2 \).
Step 5: Perform the calculation to find the moment of inertia. Ensure that the units are consistent (mass in kilograms and radius in meters) and simplify the expression to obtain the final value of \( I \).
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Moment of Inertia
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 solid disk, the moment of inertia can be calculated using the formula I = (1/2) m r², where m is the mass and r is the radius.
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Percorso guidato
11:47
Intro to Moment of Inertia
Rotational Axis
The rotational axis is the line about which an object rotates. In this case, the axis is perpendicular to the plane of the DVD and passes through its center. The choice of axis significantly affects the moment of inertia, as it determines how the mass is distributed relative to that axis.
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13:46Parallel Axis Theorem
Mass and Radius
The mass and radius of an object are critical parameters in calculating its moment of inertia. The mass (21 g) indicates how much matter is present, while the radius (6 cm, derived from the 12 cm diameter) affects how far the mass is distributed from the axis of rotation. Both factors are essential for determining the object's resistance to rotational acceleration.
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06:18Calculating Radius of Nitrogen
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