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 connects the chainring to a smaller gear, called a sprocket, which is attached to the rear wheel (see figure below). The angular velocity of the sprocket depend 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 v the cyclist travels is determined by the angular velocity of his rear wheel. Use this information to answer the following. Rear wheel Sprocket diameter Chain Chainring diameter 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 rat 90 revolutions per minute, find his speed in kilometers per hour. (1 km = 1,000,000 mm. Round your answer to one decimal place.) km/hr

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 connects the chainring to a smaller gear, called a sprocket, which is attached to the rear wheel (see figure below). The angular velocity of the sprocket depend 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 v the cyclist travels is determined by the angular velocity of his rear wheel. Use this information to answer the following. Rear wheel Sprocket diameter Chain Chainring diameter 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 rat 90 revolutions per minute, find his speed in kilometers per hour. (1 km = 1,000,000 mm. Round your answer to one decimal place.) km/hr

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter3: Radian Measure

Section3.5: Velocities

Problem 63PS: Cycling When a cyclist pedals. he turns a gear, called a chainring. The angular velocity of the...

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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)
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.
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