Domanda del libro di testo
A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. What is the speed of the tip of a blade 10 s after the fan is turned off?
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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
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Capitolo 12, Problema 1a
A high-speed drill reaches 2000 rpm in 0.50 s. What is the magnitude of the drill's angular acceleration?
Guida verificata passo dopo passo1
Step 1: Identify the given values in the problem. The drill's final angular velocity is given as 2000 rpm (revolutions per minute), and the time taken to reach this speed is 0.50 s. Convert the angular velocity to radians per second using the formula: \( \omega = \text{rpm} \times \frac{2\pi}{60} \).
Step 2: Recognize that the drill starts from rest, so the initial angular velocity \( \omega_0 \) is 0 rad/s. The angular acceleration \( \alpha \) can be calculated using the kinematic equation for rotational motion: \( \alpha = \frac{\omega - \omega_0}{t} \), where \( \omega \) is the final angular velocity, \( \omega_0 \) is the initial angular velocity, and \( t \) is the time.
Step 3: Substitute the converted value of \( \omega \) (in rad/s), \( \omega_0 = 0 \), and \( t = 0.50 \) s into the formula \( \alpha = \frac{\omega - \omega_0}{t} \).
Step 4: Simplify the expression to calculate the angular acceleration \( \alpha \). Ensure the units are consistent (radians per second squared).
Step 5: Interpret the result. The magnitude of the angular acceleration represents how quickly the drill's angular velocity increases over time.
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Angular Velocity
Angular velocity is a measure of how quickly an object rotates around an axis, typically expressed in radians per second or revolutions per minute (rpm). In this question, the final angular velocity of the drill is given as 2000 rpm, which needs to be converted to radians per second for calculations involving angular acceleration.
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Percorso guidato
06:18
Intro to Angular Momentum
Angular Acceleration
Angular acceleration refers to the rate of change of angular velocity over time. It is calculated by taking the difference between the final and initial angular velocities and dividing by the time taken for that change. In this case, the drill's angular acceleration can be determined by using the final angular velocity and the time interval of 0.50 seconds.
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Percorso guidato
12:12Conservation of Angular Momentum
Kinematic Equations for Rotational Motion
Kinematic equations for rotational motion are analogous to linear motion equations and relate angular displacement, angular velocity, angular acceleration, and time. These equations allow us to solve for unknown variables in rotational dynamics problems, such as finding angular acceleration when the final angular velocity and time are known.
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Percorso guidato
07:18Equations of Rotational Motion
Pratica correlata
Domanda del libro di testo
A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. Through how many revolutions does the fan turn while stopping?
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Domanda del libro di testo
An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60 rpm to 90 rpm in 10 s. What is the tangential acceleration of a tooth on the sprocket?
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