The 38-lb solid circular disk is initially at rest on the horizontal surface when a force P, of 7-lb, constant in magnitude and direction, is applied to the cord wrapped securely around its periphery. Friction between the disk and the surface is negligible. Calculate the angular velocity ω of the disk after the 7-lb force has been applied for 3 seconds and find the linear velocity v of the center of the disk after it has moved 6 feet from rest.

Wo audio speakers are placed on a vertical rail. speaker a is placed at head-level while speaker b is place at some variable height, \delta yδy, above speaker a. both speakers receive simultaneous input from a sine-wave generator so the speakers each produce a pure sinusoidal sound wave with a wavelength of 0.531 meters. calculate the lowest height that speaker b can be placed above speaker a to produce a minimum of sound heard by person standing \delta x = 7.86δx=7.86 meters directly in front of speaker a.

Explain the difference between each pair of concepts. a. frequency and relative frequency b. percentage and relative frequency a. select the correct choice below. a. frequency is the total number of observations in a data set. relative frequency is the number of times a particular distinct value occurs. b. frequency is the number of times a particular distinct value occurs. relative frequency is the ratio of the frequency of a value to the total number of observations. c. frequency is the total number of observations in a data set. relative frequency is the ratio of the number of times a particular distinct value occurs to the frequency. d. frequency is the number of times a particular distinct value occurs. relative frequency is the ratio of the frequency of two different values.

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.