A carousel with a 45-foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel ia radians per minute. (Round your answer to two decimal places.) radians per minute (b) Find the linear speed (in feet per minute) of the platform rim of the carousel. (Round your answer to two decimal places.) feet per minute Need Help? Read it Watch it

A carousel with a 45-foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel ia radians per minute. (Round your answer to two decimal places.) radians per minute (b) Find the linear speed (in feet per minute) of the platform rim of the carousel. (Round your answer to two decimal places.) feet per minute Need Help? Read it Watch it

Name: A carousel with a 45-foot diameter makes 4 revolutions per minute.(a)
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Description: A carousel with a 45-foot diameter makes 4 revolutions per minute.(a) Find the angular speed of the carousel in radians per minute. (Round your answer to two decimal places.)radians per minute(b) Find the linear speed (in feet per minute) of the pla

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Trigonometry

Section1.1: Radian And Degree Measure

Problem 64E: Linear and Angular Speed A 714 -inch circular power saw blade rotates at 5200 revolutions per...

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Cycling When a cyclist pedals. he turns a gear, called a chainring. The angular velocity of the chainring will determine the linear speed at which the chain travels. The chain connects the chainring to a smaller gear, called a sprocket, winch is attached to the rear wheel (Figure 11). The angular velocity of the sprocket depends upon the linear speed of the chain. The sprocket and rear wheel rotate at the same rate, and the diameter of the rear wheel is 700 millimeters. The speed at which the cyclist travels is determined by the angular velocity of his rear wheel. Use this information to answer Problems 63 through 67. On level ground, a pro cyclist would use a larger chainring and a smaller sprocket. If he shifted to a 210-millimeter-diameter chainring and a 40-millimeter-diameter sprocket, how fast would he be traveling in kilometers per hour if he pedaled at a rate of 80 revolutions per minute?
Cycling When a cyclist pedals. he turns a gear, called a chainring. The angular velocity of the chainring will determine the linear speed at which the chain travels. The chain connects the chainring to a smaller gear, called a sprocket, winch is attached to the rear wheel (Figure 11). The angular velocity of the sprocket depends upon the linear speed of the chain. The sprocket and rear wheel rotate at the same rate, and the diameter of the rear wheel is 700 millimeters. The speed at which the cyclist travels is determined by the angular velocity of his rear wheel. Use this information to answer Problems 63 through 67. Suppose a cyclist was using a 150-millimeter-diameter chainring and an 80-millimeter-diameter sprocket. How fast would she need to pedal, in revolutions per minute, in order to maintain a speed of 20 kilometers per hour?
Cycling When a cyclist pedals. he turns a gear, called a chainring. The angular velocity of the chainring will determine the linear speed at which the chain travels. The chain connects the chainring to a smaller gear, called a sprocket, winch is attached to the rear wheel (Figure 11). The angular velocity of the sprocket depends upon the linear speed of the chain. The sprocket and rear wheel rotate at the same rate, and the diameter of the rear wheel is 700 millimeters. The speed at which the cyclist travels is determined by the angular velocity of his rear wheel. Use this information to answer Problems 63 through 67. If a cyclist was using her 150-millimeter-diameter chainring and pedaling at a rate of 95 revolutions per minute, what diameter sprocket would she need in order to maintain a speed of 24 kilometers per hour?
Cycling When a cyclist pedals. he turns a gear, called a chainring. The angular velocity of the chainring will determine the linear speed at which the chain travels. The chain connects the chainring to a smaller gear, called a sprocket, winch is attached to the rear wheel (Figure 11). The angular velocity of the sprocket depends upon the linear speed of the chain. The sprocket and rear wheel rotate at the same rate, and the diameter of the rear wheel is 700 millimeters. The speed at which the cyclist travels is determined by the angular velocity of his rear wheel. Use this information to answer Problems 63 through 67. A pro cyclist is climbing Mount Ventoux, equipped with a 150-millimeter-diameter chainring and a 95-millimeter-diameter sprocket. If he was pedaling at a rate of 90 revolutions per minute, find his speed in kilometers per hour. (1km=1,000,000mm)
Fan A ceiling fan with 16-in. blades rotates at 45rpm. a Find the angular speed of the fan in rad/min. b Find the linear speed of the tips of the blades in in./min.
The circular blade on a saw has a radius of 4 inches and it rotates at 2400 revolutions per minute. a. Find the angular speed of the blade in radians per minute. b. Find the linear speed of the edge of the blade.
Linear and Angular Speed A Blu-ray disc is approximately 12 centimeters in diameter. The drive motor of a Blu-ray player is able to rotate up to 10,000 revolutions per minute. (a) Find the maximum angular speed (in radians per second) of a Blu-ray disc as it rotates. (b) Find the maximum linear speed (in meters per second) of a point on the outermost track as the disc rotates.
Linear and Angular Speed A 714 -inch circular power saw blade rotates at 5200 revolutions per minute. (a) Find the angular speed of the saw blade in radians per minute. (b) Find the linear speed (in feet per minute) of the saw teeth as they contact the wood being cut.
Linear and Angular Speed A carousel with 50-foot diameter makes 4 revolutions per minute. (a) Find the maximum angular speed (in radians per second) of a Blu-ray disc as it rotates. (b) Find the maximum linear speed (in meters per second) of a point on the outermost track as the disc rotates.
Phonograph Phonograph records are vinyl discs that rotate on a turntable. A typical record album is 12 inches in diameter and plays at 3313 revolutions per minute (a) Find the angular speed of a record album. (b) Find the linear speed (in inches per minute) of the outer edge of a record album.
Angular Speed and Linear Speed A potters wheel with radius 8 in. spins at 150rpm. Find the angular and linear speeds of a point on the rim of the wheel.
Angular Velocity A belt connects a pulley of radius 8 centimeters to a pulley of radius 6 centimeters. Each point on the belt is travelling at 24 centimeters per second. Find the angular velocity of each pulley (Figure 1 ).