Textbook Question
A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door’s moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge?
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Ch 12: Rotation of a Rigid Body
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 12, Problem 19
In FIGURE EX12.19, for what value of Xaxle will the two forces provide 1.8 Nm of torque about the axle?
Verified step by step guidance1
Step 1: Recall the formula for torque: τ = F × r × sin(θ), where F is the force, r is the distance from the axis of rotation to the point of application of the force, and θ is the angle between the force vector and the lever arm.
Step 2: Analyze the diagram. The forces F1 and F2 are applied at different points on the rectangle. F1 is applied horizontally to the left, and F2 is applied horizontally to the right. The axle is located at point A(x_A, y_A). The distances from the axle to the points of application of F1 and F2 need to be determined.
Step 3: For F1, the perpendicular distance to the axle is the vertical distance y_A. For F2, the perpendicular distance to the axle is the horizontal distance x_A. These distances will be used to calculate the torque contributions from each force.
Step 4: Write the torque equation for the system. The total torque about the axle is given as τ_total = τ_F1 + τ_F2. Substitute the values: τ_total = F1 × y_A + F2 × x_A. The total torque is specified as 1.8 Nm.
Step 5: Solve for x_A. Rearrange the equation to isolate x_A: x_A = (τ_total - F1 × y_A) / F2. Substitute the given values for τ_total, F1, y_A, and F2 to find x_A.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Torque
Torque is a measure of the rotational force applied to an object, calculated as the product of the force and the distance from the pivot point (lever arm). It is expressed in Newton-meters (Nm). The direction of the torque is determined by the direction of the force and the position of the lever arm relative to the pivot.
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Net Torque & Sign of Torque
Lever Arm
The lever arm is the perpendicular distance from the line of action of the force to the axis of rotation. In torque calculations, the lever arm is crucial because it directly influences the amount of torque produced by a given force. A longer lever arm results in greater torque for the same force.
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Equilibrium of Forces
In physics, the equilibrium of forces occurs when the sum of all forces acting on an object is zero, resulting in no net force and no acceleration. For torque, this means that the clockwise and counterclockwise torques must balance each other out, allowing for the calculation of unknown forces or distances in a system.
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Related Practice
Textbook Question
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?
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Textbook Question
An object whose moment of inertia is 4.0 kg m2 is rotating with angular velocity 0.25 rad/s. It then experiences the torque shown in FIGURE EX12.25. What is the object's angular velocity at t = 3.0s?
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Textbook Question
An object's moment of inertia is 2.0 kg m2. Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?
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Textbook Question
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 the edge of the disk?
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Textbook Question
A 4.0-m-long, 500 kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end of the beam. What is the magnitude of the torque about the bolt due to the worker and the weight of the beam?
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