A certain alarm clock ticks four times each second, with each tick representing half a period. The balance wheel consists of a thin rim I = mr? with radius 0.25m, connected to the balance staff by thin spokes of negligible mass. The total mass of the balance wheel is 0.50 g. 1. What is the moment of inertia of the balance wheel about its shaft? 2. What is the torsion constant of the coil spring?

A certain alarm clock ticks four times each second, with each tick representing half a period. The balance wheel consists of a thin rim I = mr? with radius 0.25m, connected to the balance staff by thin spokes of negligible mass. The total mass of the balance wheel is 0.50 g. 1. What is the moment of inertia of the balance wheel about its shaft? 2. What is the torsion constant of the coil spring?

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Description: A certain alarm clock ticks four times each second, with each tick representing half a period.The balance wheel consists of a thin rim I = mr? with radius 0.25m, connected to thebalance staff by thin spokes of negligible mass. The total mass of the

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 78P: Review. A string is wound around a uniform disk of radius R and mass M. The disk is released from...

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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.
A child works on a project in art class and uses an outline of her hand on a sheet of construction paper to draw a turkey (Fig. P16.36). The teacher pins the turkey to the bulletin board in the front of the classroom by using a thumbtack. The student notices that if she flicks her finger on the end of the turkey, it oscillates back and forth with a frequency of about 1.65 Hz. If the rotational inertia of the paper turkey is 1.25 105 kgm2 and its mass is 0.005 kg, what is the distance between the thumbtack and the center of mass of the turkey? FIGURE P16.36
Three forces are exerted on the disk shown in Figure P12.71,and their magnitudes are F3 = 2F2 = 2F1. The disks outer rimhas radius R, and the inner rim has radius R/2. As shown in thefigure, F1 and F3 are tangent to the outer rim of the disk, and F2 is tangent to the inner rim. F3 is parallel to the x axis, F2 is parallel to the y axis, and F1 makes a 45 angle with the negative x axis. Find expressions for the magnitude of each torque exertedaround the center of the disk in terms of R and F1. FIGURE P12.71 Problems 71-75
Disc jockeys (DJs) use a turntable in applying their trade, often using their hand to speed up or slow down a disc record so as to produce a desired change in the sound (Fig. P12.56). Suppose DJ Trick wants to slow down a record initially rotating clockwise (as viewed from above) with an angular speed of 33.0 rpm to an angular speed of 22.0 rpm. The record has a rotational inertia of 0.012 kgm2 and a radius of 0.15 m. a. What angular acceleration is necessary if he wishes to accomplish this feat in exactly 0.65 s with a constant acceleration? b. How many revolutions does the record go through during this change in speed? c. If DJ Trick applies a vertical force with his finger to the edge of the record, with what force must he push so as to slow the record in the above time? Assume the coefficient of kinetic friction between his finger and the record is 0.50, and ignore the mass of the finger. FIGURE P12.56
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 P12.64. 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 T=2[(M+2m)R2+mr22mgR]1/2 Figure P12.64
A disk with a radius of 4.5 m has a 100-N force applied to its outer edge at two different angles (Fig. P12.55). The disk has arotational inertia of 165 kg m2. a. What is the magnitude of the torque applied to the disk incase 1? b. What is the magnitude of the torque applied to the disk incase 2? c. Assuming the force on the disk is constant in each case,what is the magnitude of the angular acceleration applied tothe disk in each case? d. Which case is a more effective way of spinning the disk?Describe which quantity you are using to determine effectiveness and why you chose that quantity. FIGURE P12.55
A square plate with sides 2.0 m in length can rotatearound an axle passingthrough its center of mass(CM) and perpendicular toits surface (Fig. P12.53). There are four forces acting on the plate at differentpoints. The rotational inertia of the plate is 24 kg m2. Use the values given in the figure to answer the following questions. a. Whatis the net torque acting onthe plate? b. What is theangular acceleration of the plate? FIGURE P12.53 Problems 53 and 54.
A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.83. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. (a) What is the minimum value of h (in terms of R) such that the sphere completes the loop? (b) What are the force components on the sphere at the point P if h = 3R? Figure P10.83
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A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.8S. It starts Iron i test with the lowest point of the sphere at height h above the bottom of the loop of radius R. much larger than r. (a) What is the minimum value of h (in terms of H) such that the sphere completes the loop? (b) What are the force components on the sphere at the point p if h = 3R?
A pendulum is swinging back and forth. The angle A that the pendulum's string makes with the vertical line can be modelled by the function 0(t) = 0.15 cos(6t) a. Determine the maximum angular speed of the pendulum? When does it happen in its first oscillation? b. What is the maximum acceleration of the pendulum? When does it happen in its first oscillation?
A uniform rod of mass M and length L is free to swing back and forth by pivoting a distance x from its center. It undergoes harmonic oscillations by swinging back and forth under the influence of gravity. M = 4.6 kgL = 1.5 mx = 0.24 m a. In terms of M, L, and x, what is the rod’s moment of inertia I about the pivot point. b. Calculate the rod’s period T in seconds for small oscillations about its pivot point. c. In terms of L, find an expression for the distance xm for which the period is a minimum.