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Ch. 10 - Rotational Motion
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 10 - Rotational MotionProblem 6
Chapter 10, Problem 6

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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1
Determine the total distance traveled by the ball, which is given as 3.1 m.
Recall the relationship between the distance traveled by a rolling object and the number of revolutions it makes: \( d = n \cdot C \), where \( d \) is the distance, \( n \) is the number of revolutions, and \( C \) is the circumference of the ball.
The circumference \( C \) of a circle is related to its diameter \( D \) by the formula \( C = \pi D \). Substitute this into the distance formula: \( d = n \cdot \pi D \).
Rearrange the formula to solve for the diameter \( D \): \( D = \frac{d}{n \cdot \pi} \).
Substitute the given values: \( d = 3.1 \; \text{m} \), \( n = 12.0 \), and \( \pi \approx 3.1416 \) into the formula to calculate \( D \).

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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 its diameter.
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Revolutions and Distance

One complete revolution of a circular object corresponds to a distance equal to its circumference. Therefore, if the ball makes 12.0 revolutions, the total distance traveled can be expressed as D = number of revolutions × circumference, which is crucial for determining the diameter.
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Linear Distance Measurement

Linear distance measurement refers to the straight-line distance between two points. In this scenario, the ball rolls a total distance of 3.1 m, which is the key measurement needed to calculate the diameter of the ball based on the revolutions it completes.
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Related Practice
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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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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

(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?

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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). What is the angular velocity (rad/s) of the platter?

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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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