医学物理学-chapter2b_14_p.pptVIP

Summary to the last lecture 2.4 Momentum and its conservation（守恒） 2.4.2 momentum conservation 2.5 Circular Motion  (圆周运动) Precession 2.5 Elasticity of Materials  (Chapter 2 in the textbook) We consider a single particle moves in a central force field which is directed from or away from the origin (原点). This means that the central force has the same direction with r . Taking the gravity as an example, the gravity points to the center of the earth. This explains that Angular Momentum in a central force field is a conservative physical quantity. A simple relation between ? and the tangential velocity v can be found from the relation between ? and arc length s. Yield：be flexible under stress of physical force; Real materials always yield （变形） to some extent under the influence of applied forces; we shall now develop models to describe the relation between the deformation (变形) of real materials and the forces responsible for the deformations. The rotational kinetic energy Particle’s kinetic energy: The kinetic energy of rotation of the body should be the sum of kinetic energies taken over all the particles that make up the body. Third lecture ends here The angular momentum of a rigid body If v is a tangential velocity, and it is perpendicular to r, we could use the formula We have (第四次课从本页 到Continuity equation） O P w z m For rotations, the direction of ? is defined as right-hand rule. It should be the same as angular momentum. Can we write it as follows? Does this contradict with Do you want to know? A. Yes; B. No? What does equal to? O P w z m ? Using 0 Also from Suppose: rotation axis is z-axis, i.e. r p are in x-y plane Nuclear magnetic moment Magnetic field Precession! （旋进或进动） What is the precession angular velocity? For a spinning top, its external force is gravity only that exerts on its mass center. Therefore the torque for the spinning top is ? dt = dL Comparing it with Impulse! ? dt = dL r ? mg ?-? ? L, r mg ?-? ? ? d? Lsin??d? = dL ? =