Multiple Choice
An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through?
BONUS:How many complete revolutions does it make?
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12. Rotational Kinematics
Rotational Position & Displacement
2:48 minutesProblem 6
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?
Verified step by step guidance1
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 \( D \).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mKey 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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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 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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