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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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TOC.tableOfContents
- 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: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 10, Problema 5c
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?
Guida verificata passo dopo passo1
Convert the rotational speed from revolutions per minute (rpm) to radians per second. Use the formula: \( \omega = \frac{2\pi \cdot \text{revolutions per minute}}{60} \), where \( \omega \) is the angular velocity in radians per second.
Determine the linear velocity \( v \) of the writing head at a distance \( r = 3.00 \; \text{cm} \) (or \( 0.030 \; \text{m} \)) from the axis. Use the relationship \( v = r \cdot \omega \), where \( r \) is the radius and \( \omega \) is the angular velocity.
Calculate the number of bits that can fit in one meter of the track. Since each bit requires \( 0.50 \; \mu\text{m} \) (or \( 0.50 \times 10^{-6} \; \text{m} \)), the number of bits per meter is given by \( \text{bits per meter} = \frac{1}{0.50 \times 10^{-6}} \).
Determine the number of bits written per second by multiplying the linear velocity \( v \) (in meters per second) by the number of bits per meter. Use the formula: \( \text{bits per second} = v \cdot \text{bits per meter} \).
Combine all the results to express the final answer in terms of bits per second, ensuring all units are consistent throughout the calculation.
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Angular Velocity
Angular velocity is the rate of rotation of an object, typically measured in radians per second. In this context, the platter's rotation speed of 7200 revolutions per minute (rpm) can be converted to radians per second to determine how quickly the writing head moves across the disk surface. Understanding angular velocity is crucial for calculating the linear speed at which data can be written.
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Percorso guidato
06:18
Intro to Angular Momentum
Linear Speed
Linear speed refers to the distance traveled per unit of time along a straight path. For a rotating object, linear speed can be calculated using the formula v = rω, where v is linear speed, r is the radius (distance from the axis of rotation), and ω is the angular velocity. This concept is essential for determining how fast the writing head can move across the platter to write data.
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Percorso guidato
07:31Linear Thermal Expansion
Data Transfer Rate
Data transfer rate is the amount of data that can be written or read in a given time period, typically measured in bits per second. In this scenario, the transfer rate can be calculated by dividing the linear speed of the writing head by the length required for each bit. This concept is vital for understanding how efficiently data can be recorded on the hard drive.
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Percorso guidato
05:14Overview of Heat Transfer
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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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The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). What is the angular velocity (rad/s) of the platter?
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Domanda del libro di testo
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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