PHY183A CORE LESSONS & OUTPUT SKILLS, Summer '99

CORE LESSONS & OUTPUT SKILLS

PHY183A, Summer '99

Given a planar configuration of rigidly connected masses and an axis perpendicular to its plane, calculate its moment of inertia about the axis.

Use, and justify the use of conservation of angular momentum to solve problems involving torqueless change from one state of uniform circular motion to another.
Solve problems involving energy of rotation in circular motion, starting from the equation for kinetic energy in linear motion.
Solve problems involving power transfer in uniform circular motion, starting from the equation for power transfer in uniform linear motion.

For circular motion, differentiate s = θ r to derive the relation between linear acceleration, angular acceleration, and radius.
Starting from Newton's second law, derive the relation between torque, moment of inertia, and angular acceleration for a point mass in circular motion.
For circular motion with constant angular acceleration, derive the general expressions for angular velocity and angular acceleration as functions of time (involves integrals). Check the answers by differentiation.
For circular motion with constant angular acceleration, eliminate the time variable between the angular displacement and angular velocity expressions to obtain angular velocity as a function of angular displacement and angular acceleration.

Solve planar constant-angular-acceleration problems involving torque, moment of inertia, angular velocity, rotational displacement, and time.

Define the torque and angular momentum vectors for (a) a single particle (b) a system of particles.
Starting from Newton's 2nd law, derive its rotational analog and state when it can be written as a scalar equation.
Start from the equation for linear kinetic energy and derive the corresponding one for rotational kinetic energy.
Explain why conservation of angular momentum may not hold in one system but may if the system is expanded.

For masses in circular motion at fixed radii, solve problems relating torque, moment of inertia, angular acceleration, rotational kinetic energy, work, and angular momentum.
Given a system in which angular momentum is changing with time due to a specified applied torque, reconstruct the minimum expanded system in which total angular momentum is conserved. Describe the reaction torque which produces the compensating change in angular momentum.

Vocabulary: Newton's law of universal gravitation, universal gravitational constant.
Use Newton's law of universal gravitation, your correctly remembered value of g, and a solar system data table, to calculate the value of the universal gravitational constant G.

Calculate the vector gravitational force on one mass due to a given configuration of other masses.

Vocabulary: apogee, central force, perigee.
State Kepler's three kinematical laws of planetary motion.
State how Newton's law of universal gravitation may be used to justify Kepler's laws.

Given a table of solar system data, use Newton's law of universal gravitation and the value of g at the earth's surface to determine the period of revolution, orbital speed, and centripetal acceleration of a given circularly orbiting satellite.

Vocabulary: sound wave, longitudinal wave, transverse wave, compressions, rarefactions, bulk modulus (of elasticity), Young's modulus, stress, strain.
Starting with Newton's second law, derive the expression relating the net force on an element of mass of a stretched string to the transverse acceleration of that string. Comparing the resultant expression to the one-dimensional wave equation, find the expression for the speed of a transverse wave in a stretched string.
Determine the speed of the waves (in terms of the properties of the medium), given the differential wave equations describing: (i) transverse waves in a stretched string; (ii) longitudinal compressional waves in a solid or a gas.

For a given harmonic (sinusoidal) disturbance write down the equation representing the waveform and calculate the wavelength and frequency of the wave for: (i) transverse waves in a stretched string; and (ii) longitudinal compressional waves in a solid or a gas.

Vocabulary: decibel, plane wave, spherical wave, wave intensity, wave vector, wave front.
State the expression for the intensity of a plane wave and the power transmitted across a given cross-sectional area of the medium through which the wave travels.

For intensity calculations associated with plane and spherical waves, use the unit of intensity level, the decibel.

For an acoustic plane wave of given amplitude and frequency, traveling through an elastic medium of given mass density and elasticity, calculate the wave's intensity, energy density, and rate at which it propagates energy.
Given the intensity of a spherical wave at one radial distance from the wave source, calculate the wave's intensity at any other radial distance.

Vocabulary: antinode, characteristic (resonant) frequency, first overtone, fundamental frequency, harmonics, node, normal modes, overtones, standing wave, superposition.

Given a set of physical boundary conditions, determine the possible frequencies of the normal modes for transverse standing waves on a stretched string. For a string of given mass per unit length under a given tension, determine the numerical values for some of these frequencies.
For longitudinal sound waves in a closed organ pipe, apply the appropriate boundary conditions to determine the possible frequencies for standing waves. Do the same for an open pipe. Determine the numerical values of the fundamental frequency and some of its lower harmonics.