Velocity Task Introduction: The pedal of a bicycle is attached to a crank arm that revolves when the pedal is pushed by a person's foot. As the crank arm turns, it pulls a chain that is attached to the rear wheel of the bicycle, causing the bicycle to move forward. G 118 18 cm 16 cm A particular bicycle has wheels that are 66 cm in diameter. The radius of the crank arm is 18 cm. At its lowest point, the pedal is 16 cm above the ground. A person is pedaling the bicycle such that the crank arm rotates once every second. Questions: 1. Write an equation that models the vertical position of the foot with respect to the ground, starting from the lowest point, as the crank arm turns. 2. What is the rate of change of the vertical position of the foot when it is at the midline? Explain your answer 3. How fast, in kilometres per hour, is the bicycle moving? 4. Determine an equation that would model the foot's position when the cyclist is traveling 5 km/h. Compare this equation to your equation from question 1 and explain any differences. 5. Use calculus to explain why the rotation velocity of a point on the perimeter of a wheel is the same as the velocity of the pedal. Use examples to support your answer.

Velocity Task Introduction: The pedal of a bicycle is attached to a crank arm that revolves when the pedal is pushed by a person's foot. As the crank arm turns, it pulls a chain that is attached to the rear wheel of the bicycle, causing the bicycle to move forward. G 118 18 cm 16 cm A particular bicycle has wheels that are 66 cm in diameter. The radius of the crank arm is 18 cm. At its lowest point, the pedal is 16 cm above the ground. A person is pedaling the bicycle such that the crank arm rotates once every second. Questions: 1. Write an equation that models the vertical position of the foot with respect to the ground, starting from the lowest point, as the crank arm turns. 2. What is the rate of change of the vertical position of the foot when it is at the midline? Explain your answer 3. How fast, in kilometres per hour, is the bicycle moving? 4. Determine an equation that would model the foot's position when the cyclist is traveling 5 km/h. Compare this equation to your equation from question 1 and explain any differences. 5. Use calculus to explain why the rotation velocity of a point on the perimeter of a wheel is the same as the velocity of the pedal. Use examples to support your answer.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 6OQ: Consider an object on a rotating disk a distance r from its center, held in place on the disk by...

See similar textbooks

Similar questions

The dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigroaeneus has a radius of 2.00 cm and is rolled by the beetle at 6.25 cm/s. (a) What is the rolling balls angular speed? (b) How many full rotations are required if the beetle rolls the ball a distance of 1.00 m?
A boy rides his bicycle 2.00 km. The wheels have radius 30.0 cm. What is the total angle the tires rotate through during his trip?
A rope of negligible mass is wrapped around a 225 kg solid cylinder of radius 0.400 m. The cylinder is suspended several meters off the ground with its axis oriented horizontally, and turns on that axis without friction, (a) If a 75.0-kg man takes hold of the free end of the rope and falls under the force of gravity, what is his acceleration? (b) What is the angular acceleration of the cylinder? (c) if the mass of the rope were not neglected, what would happen to the angular acceleration of the cylinder as the man falls?
Integrated Concepts An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is its angular acceleration in rad/s2? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the radial acceleration in m/s2 and multiples of g of this point at full rpm?
Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness, (a) If a human centrifuge has a radius of 4.50 m, what angular speed results in a centripetal acceleration of 9g? (b) What linear speed would a person in the centrifuge have at this acceleration?
An ultracentrifuge accelerates from to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s2 ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of totation of the ultracentrifuge?
Find the net torque on the wheel in Figure P10.23 about the axle through O, taking a = 10.0 cm and b = 25.0 cm. Figure P10.23
At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?
Figure P12.67 shows a vertical force applied tangentially to a uniform cylinder of weight Fg. The coefficient of static friction between the cylinder and all surfaces is 0.500. The force P is increased in magnitude until the cylinder begins to rotate. In terms of Fg find the maximum force magnitude P that can be applied without causing the cylinder to rotate. Suggestion: Show that both friction forces will be at their maximum values when the cylinder is on the verge of slipping.
One method of pitching a softball is called the wind-mill delivery method, in which the pitchers arm rotates through approximately 360 in a vertical plane before the 198-gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 98.0 mi/h. Assume the angular acceleration is uniform throughout the pitching motion and take the distance between the softball and the shoulder joint to be 74.2 cm. (a) Determine the angular speed of the arm in rev/s at the instant of release, (b) Find the value of the angular acceleration in rev/s2 and the radial and tangential acceleration of the ball just before it is released, (c) Determine the force exerted on the ball by the pitchers hand (both radial and tangential components) just before it is released.
A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?
While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75kgm2 and its rotational kinetic energy is 175 J. (a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter’s shoe if it is 1.05 m from the hip joint?