Textbook Question
(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?
2
views
Ch. 10 - Rotational Motion
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
Not the one you use?Change textbookSelect a different textbook
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 5b
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?
Verified step by step guidance1
Convert the rotational speed from revolutions per minute (rpm) to revolutions per second (rps). Use the conversion factor: 1 minute = 60 seconds. The formula is: \( \text{rps} = \frac{\text{rpm}}{60} \).
Determine the angular velocity \( \omega \) in radians per second. Use the relationship \( \omega = 2\pi \times \text{rps} \), where \( 2\pi \) radians correspond to one full revolution.
Identify the radius \( r \) of the circular path. The problem states that the reading head is located 3.00 cm from the rotation axis, so \( r = 3.00 \, \text{cm} = 0.030 \, \text{m} \) (convert to meters for consistency in SI units).
Use the formula for linear speed \( v \): \( v = r \cdot \omega \), where \( r \) is the radius and \( \omega \) is the angular velocity. Substitute the values of \( r \) and \( \omega \) into this equation.
Simplify the expression to find the linear speed \( v \). Ensure the units are consistent (meters per second, \( \text{m/s} \)).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angular Velocity
Angular velocity is a measure of how quickly an object rotates around an axis, typically expressed in radians per second. In this context, the hard drive platter's rotation speed of 7200 revolutions per minute (rpm) can be converted to angular velocity, which is essential for calculating linear speed. The formula to convert rpm to radians per second is: ω = (rpm × 2π) / 60.
Recommended video:
Guided course
06:18
Intro to Angular Momentum
Linear Speed
Linear speed refers to the distance traveled per unit of time by a point on a rotating object. It can be calculated using the formula v = rω, where v is the linear speed, r is the radius (distance from the axis of rotation), and ω is the angular velocity. In this case, the linear speed of the point on the platter is determined by its distance from the rotation axis and the angular velocity derived from the platter's rpm.
Recommended video:
Guided course
07:31Linear Thermal Expansion
Centripetal Motion
Centripetal motion describes the motion of an object moving in a circular path, requiring a net inward force to maintain that path. In the context of the hard drive platter, the reading head experiences centripetal acceleration due to the circular motion of the platter. Understanding this concept is crucial for analyzing forces acting on the reading head and ensuring it remains properly aligned with the rotating platter.
Recommended video:
Guided course
06:48Intro to Centripetal Forces
Related Practice
Textbook Question
(I) A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle θ (Fig. 10–50) of 1.4 x 10-5 rad. What diameter spot will it make on the Moon?
2
views
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?
3
views
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?
2
views
Textbook Question
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?
7
views