Multiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius -0.118 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.50 s. Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. Us - Number 210 Units m

Multiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius -0.118 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.50 s. Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. Us - Number 210 Units m

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter13: Rotation Ii: A Conservation Approach

Section: Chapter Questions

Problem 27PQ: The motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis...

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Keratinocytes are the most common cells in the skins outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body diameter of 1.00 105 m (10 m), what minimum angular speed would be required to produce the observed linear speed of 1.67 107 m/s (10 m/min)? (b) How many complete revolutions would be required for the cell to roll a distance of 5.00 103 m? (Because of slipping as the cells roll, averages of observed angular speeds and the number of complete revolutions are about three times these minimum values.)
The motion of spinning a hula hoop around one's hips can bemodeled as a hoop rotating around an axis not through the center, but offset from the center by an amount h, where h is lessthan R, the radius of the hoop. Suppose Maria spins a hula hoopwith a mass of 0.75 kg and a radius of 0.62 m around her waist.The rotation axis is perpendicular to the plane of the hoop, butapproximately 0.40 m from the center of the hoop. a. What isthe rotational inertia of the hoop in this case? b. If the hula hoopis rotating with an angular speed of 13.7 rad/s, what is its rotational kinetic energy?
Why is the following situation impossible? A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he slips out of his seat and climbs to the top of the rides structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of = 20.0 with the horizontal as shown in Figure P6.32. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point d = 5.32 m down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is 0.700. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. As a result, the sitting, pouting boy rotates in a circular path at a speed of 3.75 m/s. Figure P6.32
A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.0 cm as shown in Figure P6.48. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle that the radial line, from the center of the loop to the bead, makes with the vertical. (a) At what angle up from the bottom of the circle can the bead slay motionless relative to the turning circle? (b) What If? Repeat the problem, this time taking the period of the circles rotation as 0.850 s. (c) Describe how the solution to part (b) is different from the solution to part (a). (d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? (e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem. Figure P6.48
Why is the following situation impossible? A space station shaped like a giant wheel has a radius of r = 100 m and a moment of inertia of 5.00 108 kg m2. A crew of 150 people of average mass 65.0 kg is living on the rim, and the stations rotation causes the crew to experience an apparent free-fall acceleration of g (Fig. P10.52). A research technician is assigned to perform an experiment in which a ball is dropped at the rim of the station every 15 minutes and the time interval for the ball to drop a given distance is measured as a test to make sure the apparent value of g is correctly maintained. One evening, 100 average people move to the center of the station for a union meeting. The research technician, who has already been performing his experiment for an hour before the meeting, is disappointed that he cannot attend the meeting, and his mood sours even further by his boring experiment in which every time interval for the dropped ball is identical for the entire evening.
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.
An air puck of mass m1 = 0.25 kg is tied to a siring and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 1.0 kg is tied to it (Fig. P7.27). The suspended mass remains in equilibrium while the puck on the tabletop revolves, (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck? Figure P7.27
Case Study For each acceleration listed, state the position and velocity of the disk in Crall and Whipples experiment (Figs. 16.316.5). There may be more than one possible answer for each given acceleration. a. ay = 3.8 m/s2 b. ay = 3.8 m/s2 c. ay = 0
Additional Problems A typical propeller of a turbine used to generate electricity from the wind consists of three blades as in Figure P8.75. Each blade has a length of L = 35 in and a mass of m = 420 kg. The propeller rotates at the rate of 25 rev/min. (a) Convert the angular speed of the propeller to units of rad/s. Find (b) the moment of inertia of the propeller about the axis of rotation and (c) the total kinetic, energy of the propeller. Figure P8.75
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) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of 6.4106 m at its equator, what is the linear velocity at Earth's surface?
During a certain time interval, the angular position of a swinging door is described by = 5.00 + 10.0t + 2.00t2, where is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door (a) at t = 0 and (b) at t = 3.00 s.