The wheel in the figure has eight equally spaced spokes and a radius of 43 cm. It is mounted on a fixed axle and is spinning at 1.1 rev/s. You want to shoot a 25-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have? Number i Units

The wheel in the figure has eight equally spaced spokes and a radius of 43 cm. It is mounted on a fixed axle and is spinning at 1.1 rev/s. You want to shoot a 25-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have? Number i Units

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 71P: The reel shown in Figure P10.71 has radius R and moment of inertia I. One end of the block of mass m...

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Consider two objects with m1 m2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as shown in Figure P10.44. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time.
Problems 62 and 63 are paired. 62. C A disk is rotating around a fixed axis that passes through its center and is perpendicular to the face of the disk. Consider a point on the rim of the disk (point R) and another point halfway between the center and the rim (point H) at one particular instant. a. How does the angular speed v of the disk at point H compare with the angular speed of the disk at point R? b. How does the tangential speed of the disk at point H compare with the tangential speed of the disk at point R? c. Suppose we pick a point H on the disk at random (by throwing a dart, for example), and we compare the speeds at that point with the speeds at point R. How will the answers to parts (a) and (b) be different? Explain.
A turntable (disk) of radius r = 26.0 cm and rotational inertia0.400 kg m2 rotates with an angular speed of 3.00 rad/s arounda frictionless, vertical axle. A wad of clay of mass m =0.250 kg drops onto and sticks to the edge of the turntable.What is the new angular speed of the turntable?
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?
In testing an automobile tire for proper alignment, a technicianmarks a spot on the tire 0.200 m from the center. He then mountsthe tire in a vertical plane and notes that the radius vector to thespot is at an angle of 35.0 with the horizontal. Starting from rest,the tire is spun rapidly with a constant angular acceleration of 3.00 rad/s2. a. What is the angular speed of the wheel after 4.00 s? b. What is the tangential speed of the spot after 4.00 s? c. What is the magnitude of the total accleration of the spot after 4.00 s?" d. What is the angular position of the spot after 4.00 s?
A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on a horizontal section of a track as shown in Figure P10.62. It rolls around the inside of a vertical circular loop of radius r = 45.0 cm. As the ball nears the bottom of the loop, the shape of the track deviates from a perfect circle so that the ball leaves the track at a point h = 20.0 cm below the horizontal section. (a) Find the balls speed at the top of the loop. (b) Demonstrate that the ball will not fall from the track at the top of the loop. (c) Find the balls speed as it leaves the track at the bottom. What If? (d) Suppose that static friction between ball and track were negligible so that the ball slid instead of rolling. Would its speed then be higher, lower, or the same at the top of the loop? (e) Explain your answer to part (d). Figure P10.62
The angular velocity of a flywheel with radius 1.0 m varies according to (t)=2.0t . Plot ac(t) and at(t) from t=0 to 3.0 s for r=1.0m . Analyze these results to explain when acat and when acat for a point on the flywheel at a radius of 1.0 m.
An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel as shown in Figure P10.37. The flywheel is a solid disk with a mass of 80.0 kg and a radius R = 0.625 m. It turns on a frictionless axle. Its pulley has much smaller mass and a radius of r = 0.230 m. The tension Tu in the upper (taut) segment of the belt is 135 N, and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find the tension in the lower (slack) segment of the belt. Figure P10.37
A solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?
Lara is running just outside the circumference of a carousel, looking for her favorite horse to ride, with a constant angular speed of 1.00 rad/s. Just as she spots the horse, one-fourth of the circumference ahead of her, the carousel begins to move, accelerating from rest at 0.050 rad/s2. a. Taking the time when the carousel begins to move as t = 0, when will Lara catch up to the horse? b. Lara mistakenly passes the horse and keeps running at constant angular speed. If the carousel continues to accelerate at the same rate, when will the horse draw even with Lara again?
A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on a horizontal section of a track as shown in Figure P10.33. It rolls around the inside of a vertical circular loop of radius r = 45.0 cm. As the ball nears the bottom of the loop, the shape of the track deviates from a perfect circle so that the ball leaves the track at a point h = 20.0 cm below the horizontal section. (a) Find the balls speed at the top of the loop. (b) Demonstrate that the ball will not fall from the track at the top of the loop. (c) Find the balls speed as it leaves the track at the bottom. (d) What If? Suppose that static friction between ball and track were negligible so that the ball slid instead of rolling. Describe the speed of the ball at the top of the loop in this situation. (e) Explain your answer to part (d). Figure P10.33
A uniform cylindrical grindstion has a mass of 10 kg and a radius of 12 cm. (a) What is the rotational kinetic energy of the grindstone when it is rotating at 1.5103rev/min ? (b) After the grindstone’s motor is turned off, a knife blade is pressed against the outer edge coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.