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[...]... conditions to study only the motion of the center of gravity of the body, without taking the spatial distribution of its mass into account ➤ In the mathematical description of motion without rotation, every rigid body can be replaced by a point mass located in the center of gravity of the rigid body (see p 94) ■ For the description of planetary motion in the solar system, it often suffices to consider the... atomic clocks 2 Time units Second, s, SI (International System of Units) unit of time One of the basic units of the SI, defined as 9,192,631,770 periods of the electromagnetic radiation from the transition between the hyperfine structure levels of the ground state of Cesium 133 (relative accuracy: 10−14 ) Originally defined as the fraction 86400−1 of a mean solar day, subdivided into 24 hours, each hour comprising... Parameter representation of the motion on a shortened cycloid by the rolling angle φ as function of time t 7 Degrees of freedom of a mechanical system, number of independent quantities that are needed to specify the position of a system definitely ■ A point mass in 3D space has three translational degrees of freedom (displacements in three independent directions x, y, z) A free system of N mass points in... Figure 1.9: Motion on a circle of radius R Element of rotation angle: ϕ, element of arc length: s = R · ϕ b) Example: Point on rolling wheel The trajectory of a point at the distance a < R from the axis of a wheel (radius R) that rolls to the right with constant velocity is a shortened cycloid The parameter representation of a shortened cycloid in Cartesian coordinates in terms of the rolling angle φ(t)... 19.6.1 Equation of state of the ideal gas 19.6.2 Equation of state of real gases 19.6.3 Equation of states for liquids and solids 623 623 623 624 625 627 627 629 634 637 640 641 641 641 642 643 644 647 648 649 650 651 651 652 653 653 655 657 657 658 661 661 665 671 20 Heat, conversion of energy and changes of state 20.1 Energy... remain two degrees of freedom The point mass has only one degree of freedom if the motion is restricted to the x-axis (conditions: y = 0, z = 0) 8 1 Kinematics A system of two mass points that are rigidly connected by a bar of length l has f = 6 − 1 = 5 degrees of freedom (condition: (r1 − r2 )2 = l 2 , r1 , r2 : position vectors of the mass points) A rigid body has six degrees of freedom: three translational... (gyroscope), there remain three degrees of freedom of rotation A rigid body that can only rotate about a fixed axis is a physical pendulum with only one rotational degree of freedom A non-rigid continuous mass distribution (continuum model of a deformable body) has infinitely many degrees of freedom 1.1.2 Time 1 Definition and measurement of time Time, t, for quantification of processes varying with time Periodic... who helped with the revisions of the entire book Part I Mechanics 1 Kinematics Kinematics, the theory of the motion of bodies Kinematics deals with the mathematical description of motion without considering the applied forces The quantities position, path, time, velocity and acceleration play central roles 1.1 Description of motion Motion, the change of the position of a body during a time interval... screw, often with a nonius scale for more accurate reading) Interferometer: for precise optical measurement of length (see p 383) in which the wavelength of monochromatic light is used as scale 10 1 Kinematics Sonar: for acoustical distance measurement by time -of- flight measurement of ultrasound for ships; used for distance measurements with some cameras Radar: for distance measurement by means of time -of- flight... r rad m m angle length of circular arc radius Figure 1.12: Determination of the angle φ between the straight lines g1 and g2 by measurement of the arc length l and radius r , l = r · φ S: vertex 2 Angle units a) Radian, rad, SI unit of plane angle 1 rad is the angle for which the length of the circular arc connecting the endpoints of the sides just coincides with the length of a side A full circle . Equations of state 661 19.6.1 Equation of state of the ideal gas 661 19.6.2 Equation of state of real gases 665 19.6.3 Equation of states for liquids and solids 671 20 Heat, conversion of energy. 275 8.4 Superposition of vibrations 277 8.4.1 Superposition of vibrations of equal frequency 277 8.4.2 Superposition of vibrations of different frequencies 279 8.4.3 Superposition of vibrations in. access to the facts and formulas of physics. Compiled by professional scientists, engineers, and lecturers who are experts in the day- to-day use of physics, this Handbook covers topics from classical