Ski Lift An engineering firm is designing a ski lift. The wire rope needs to travel witha linear velocity of 2.0 meters per second, and the angular velocity of the bullwheelwill be 10 revolutions per minute. What diameter bullwheel should be used to drive thewire rope?

Ski Lift An engineering firm is designing a ski lift. The wire rope needs to travel witha linear velocity of 2.0 meters per second, and the angular velocity of the bullwheelwill be 10 revolutions per minute. What diameter bullwheel should be used to drive thewire rope?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Trigonometry

Section1.1: Radian And Degree Measure

Problem 7ECP: The circular blade on a saw has a radius of 4 inches and it rotates at 2400 revolutions per minute....

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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.
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)
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The first gear in a single-stage gear train has 42 teeth and an angular velocity of 2 revolutions per second. The second gear has 7 teeth. Find the angular velocity of the second gear.
Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.
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.
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.
Velocity Pitcher Aroldis Chapman threw a pitch with a recorded velocity of 105 miles per hour. Assuming he threw the pitch at an angle of 3.5 below the horizontal, find the vertical and horizontal components of the velocity. (Source: Guinness World Records)