Question

Two pulleys, one with radius 2 inches and the other with radius 8 inches. are connected by a belt. (See the figure.) If the 2 -inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8 -inch pulley.

Name: Problem 113, Chapter 7: Algebra and Trigonometry
Uploaded: 2020-06-15T16:39:59-08:00
Duration: 1 min 31 s
Channel: Katelyn Chen
Description: Two pulleys, one with radius 2 inches and the other with radius 8 inches. are connected by a belt. (See the figure.) If the 2 -inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8 -inch pulley.

   Two pulleys, one with radius 2 inches and the other with radius 8 inches. are connected by a belt. (See the figure.) If the 2 -inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8 -inch pulley.

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 7, Problem 113

Instant Answer

Solved by Expert Katelyn Chen

06/15/2020

Step 1

We have two pulleys, one with a radius of 2 inches (R1) and the other with a radius of 8 inches (R2). The smaller pulley is rotating at a speed of 3 revolutions per minute. We are asked to find the rotational speed of the larger pulley. Show more…

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Two pulleys, one with radius 2 inches and the other with radius 8 inches. are connected by a belt. (See the figure.) If the 2 -inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8 -inch pulley.

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Key Concepts

Belt-Driven Pulley Systems

This key concept involves the use of pulleys connected by a belt to transfer rotational motion from one pulley to another. The critical understanding here is that the belt maintains a constant linear speed as it moves between pulleys, despite differences in the pulleys' sizes, which results in an inverse relationship between the pulley radius and its rotational speed.

Angular Velocity and Linear Speed Relationship

This concept explains that the linear speed at the circumference of a rotating object is the product of its angular velocity and its radius. In systems where two bodies are connected by a belt, their circumferential (linear) speeds are equal, which allows us to relate the different angular velocities based on their respective radii.

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