10-30 Determine the second moment of the shaded areashown in Fig. P10-30 with respect toа.The x-axis.b. The y-axis.y60 mm60 mm30 mm60 mm60 mmFig. P10-30

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Answered: 0-30 Determine the second moment of the…

0-30 Determine the second moment of the shaded area hown in Fig. P10-30 with respect to . The x-axis. . The y-axis. y 60 mm 60 mm 30 mm 60 mm 60 mm

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter10: Rotational Motion And Angular Momentum

Section: Chapter Questions

Problem 19CQ: When there is a global heating trend on Earth, the atmosphere expands and the length of the day...

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A smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of radius R and mass M as shown in Figure P15.48. The center of the small disk is located at the edge of the large disk. The large disk is mounted at its center on a frictionless axle. The assembly is rotated through a small angle from its equilibrium position and released. (a) Show that the speed of the center of the small disk as it passes through the equilibrium position is v=2[Rg(1cos)(M/m)+(r/R)2+2]1/2 (b) Show that the period of the motion is v=2[(M/2m)+R2+mr22mgR]1/2 Figure P15.48
When there is a global heating trend on Earth, the atmosphere expands and the length of the day increases very slightly. Explain why the length of a day increases.
A thin, spherical shell of mass m and radius R rolls down aparabolic path PQR from height H without slipping (assumeR H) as shown in Figure P13.65. Path PQ is rough (and sothe shell will roll on that path), whereas path QR is smooth, orfrictionless (so the shell will only slide, not roll, in this region).Determine the height h above point Q reached by the shell onpath QR. FIGURE P13.65
A uniform solid sphere of mass m and radius r is releasedfrom rest and rolls without slipping on a semicircular ramp ofradius R r (Fig. P13.76). Ifthe initial position of the sphereis at an angle to the vertical,what is its speed at the bottomof the ramp? FIGURE P13.76
A nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.
Consider the disk in Problem 71. The disks outer rim hasradius R = 4.20 m, and F1 = 10.5 N. Find the magnitude ofeach torque exerted around the center of the disk. FIGURE P12.71 Problems 71-75
Figure P10.18 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a from sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road, (d) What pieces of data, if any, are not necessary for the calculations?
Figure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road. (d) What pieces of data, if any, are not necessary for the calculations? Figure P10.16
A piece of mud is initially at point A on the rim of a bicycle wheel of radius R rotating clockwise about a horizontal axis at a constant angular speed (Fig. P7.8). The mud dislodges from point A when the wheel diameter through A is horizontal. The mud then rises vertically and returns to point A. (a) Find a symbolic expression in terms of R, , and g for the total time the mud is in the air and returns to point .A. (b) If the wheel makes one complete resolution in the time it takes the mud to return to point A, Find an expression for the angular speed of the bicycle wheel in terms of , g, and R. Figure P7.8 Problems 8 and 69.
Two planets X and Y travel counterclockwise in circular orbits about a star as shown in Figure P13.22. The radii of their orbits are in the ratio 3:1. At one moment, they are aligned as shown in Figure P13.22a, making a straight line with the star. During the next five years, the angular displacement of planet X is 90.0 as shown in Figure F13.22b. What is the angular displacement of planet Y at this moment? Figure P13.22
Figure P10.41 shows a side view of a car tire before it is mounted on a wheel. Model it as having two side-walls of uniform thickness 0.635 cm and a tread wall of uniform thickness 2.50 cm and width 20.0 cm. Assume the rubber has uniform density 1.10 103 kg/m3. Find its moment of inertia about an axis perpendicular to the page through its center. Figure P10.41
If a loop of chain is spun at high speed, it can roll along the ground like a circular hoop without collapsing. Consider a chain of uniform linear mass density whose center of mass travels to the right at a high speed 0 as shown in Figure P16.67. (a) Determine the tension in the chain in terms of and 0. Assume the weight of an individual link is negligible compared to the tension, (b) If the loop rolls over a small bump, the resulting deformation of the chain causes two transverse pulses to propagate along the chain, one moving clockwise and one moving counterclockwise. What is the speed of the pulses traveling along the chain? (c) Through what angle does each pulse travel during the time interval over which the loop makes one revolution?