Textbook Question
How fast (in rpm) must a centrifuge rotate if a particle 8.0 cm from the axis of rotation is to experience an acceleration of 100,000 g’s?
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Ch. 10 - Rotational Motion
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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Table of contents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
Chapter 10, Problem 10.6
(II) A child rolls a ball on a level floor 3.1 m to another child. If the ball makes 12.0 revolutions, what is its diameter?
Verified step by step guidance1
Calculate the circumference of the ball using the formula for the circumference of a circle, which is \(C = 2\pi r\), where \(r\) is the radius of the ball. Since the diameter \(d = 2r\), the formula can also be written as \(C = \pi d\).
Determine the total distance the ball travels using the number of revolutions and the circumference. The total distance \(D\) traveled by the ball is the product of the number of revolutions and the circumference, \(D = \text{number of revolutions} \times C\).
Set up the equation using the given total distance traveled by the ball (3.1 m) and the expression for \(D\) from step 2. Substitute \(D = 3.1 \text{ m}\) and solve for the diameter \(d\).
Rearrange the equation to isolate \(d\) on one side. This can be done by dividing both sides of the equation by \(\pi\) and the number of revolutions.
Simplify the equation to find the expression for the diameter \(d\) of the ball.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Circumference of a Circle
The circumference of a circle is the distance around it, calculated using the formula C = πd, where d is the diameter. In this problem, knowing the circumference is essential to relate the number of revolutions the ball makes to the distance it travels.
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Circumference, Period, and Frequency in UCM
Revolutions and Distance
One complete revolution of a circular object corresponds to a distance equal to its circumference. Therefore, if a ball makes multiple revolutions, the total distance traveled can be found by multiplying the number of revolutions by the circumference. This relationship is crucial for determining the diameter from the given distance.
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Unit Conversion
In physics problems, it is often necessary to ensure that all measurements are in compatible units. In this case, the distance traveled by the ball (3.1 m) and the diameter must be expressed in the same unit system, typically meters, to accurately calculate the diameter based on the revolutions made.
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Related Practice
Textbook Question
The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–52. The wheel has angular velocity ω₁ = 48.0 rad/s about its axle, and the turntable has angular velocity ω₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) What are the directions of and at the instant shown?
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Textbook Question
A turntable of radius R₁ is turned by a circular rubber roller of radius R₂ in contact with it at their outer edges. What is the ratio of their angular velocities, ω₁/ω₂?
Textbook Question
A child rolls a ball on a level floor 3.1 m to another child. If the ball makes 12.0 revolutions, what is its diameter?
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Textbook Question
The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). If a single bit requires 0.50 μm of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?
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Textbook Question
The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it?
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