- at the end of the 19th century on his initiative.. - ~:"'at all times of the year. - ificant degree, the rotation of the Earth. - This slowing down of the Earth's rotation is so insig-. - Physical Bodies 20 The definition of the second is quite similar. - (the force with which the horse pushes off from the road) exceeds that of the inter- action "waggon-horse". - The total velocity of the boat is shown in Figure 1.5.. - weight of the package and the force that the person exerts on it.. - ratio of the corresponding sides of the force triangle. - of the 17th century.. - mained inviolable until the beginning of the 20th century. - Newton devised a powerful method of the mathematical investigation of nature. - The distance travelled grows in proportion to the square of the time.. - Substituting the time of the motion t = (v - vo)/a in s = (1/2) (v o + v) t, we obtain:. - 2nv of the circle. - For a constant radius of rotation, the acceleration is proportional to the square of the speed. - from the centre of the Earth)-about 6600 km = 6.6 X 10 6 m. - floor, and the motion of the elevator is slowing down. - The motion of the elevato.r speeds up. - Let us add this force to that of the Earth's gravitation.. - I t is inclined at an acute angle to the direction of the motion. - The minimum radius of the loop becomes equal to 4 km.. - his vertical does not coincide with that of the Earth. - latter increases) and the radius of the circle (it increases as the latter decreases). - Therefore, the directions of the "verticals". - The surface of the rotating liquid is precisely a paraboloid. - However, the direction of the vertical will change during the walk.. - is the lateral surface of the drum. - This contraction of the Earth was caused by thevery. - In fact, it is exerted on all the particles of the Earth. - five positions of the laboratory with respect to the rectilinear trajectory are shown in the figure. - The points which mark the ends of the arrows. - This force is always perpendicular to the axis of rotation and the direction of the motion. - here the direction of the motion forms right angles with the Earth's axis.. - Let us compute the magnitude of the deflection at the equator. - The cause lies in the action of the Coriolis force. - The product of the force by the duration of its action is equal to the change in the momentum of the body.. - Let us recall the vector nature of the law of conservation of momentum. - The rocket moves in the direction opposite to that of the gas stream.. - In fact, it assumes that the mass of the rocket is constant. - Since the initial speed of the acrobat is equal to zero, we have v 2. - 2gh at the top of the loop. - the moment of the break is depicted. - Let us express the work A in terms of the magnitude of the force.. - The product ma is equal to the component of the total force in the direction of the motion. - The tangential component of the force in the direction of the motion will be negative. - does not depend on the form of the path. - coincides with the form of the path "back". - We therefore look for another solu- tion of the equation. - Hence, the speed of the motion increases too. - The ratios of the corresponding legs are equal. - Oscillations 135 magnitude of the deflection of the pendulum from- ~t'8~'. - This displacement is called the ampli- tude of the oscillation.. - The argument of the sine is equal to the product of 2rc by tIT. - the dis- placement y is equal to the radius a of the circle. - This is the amplitude of the oscillation of the shadow.. - Let the period of the motion of the bob (which, of course, is also the period of oscillation of the shadow) be T. - 2n/T~ and so the instantaneous speed of the vibrating. - Denote the magnitude of the displacement of the bob by x. - The ratio of the corresponding legs is equal to the ratio of the hypotenuses, i.e.. - We arrive at the following conclusion: the magnitude of the restoring. - Let us check the correctness of the formula we have just d-erived. - (X2+ X.)(XZ-Xf)= kxatkxl (X2- xf) But X 2 - Xl is the length of the path covered by the body,. - Therefore, the magni- tude of the elastic force is directly proportional to the displacement: F = kx,. - It is now the stiffness of the spring. - An increase in the mass of the load has the same effect.. - The total energy of the vibration, remaining constant.. - Sound is a vibration of the air.. - The period of harmonic oscillations is independent of the amplitude.. - Now deflect and release one of the short pendulums. - Pull one of the spokes. - The point of application of the force has changed.. - Projecting the force onto the direction of the motion, i.e. - where r is the distance from the axis of rotation to the point of application of the force. - action of the force. - the work is equal to the product of the torque by the angle of rotation.. - The lever arm of the torque one. - If the points of application of the forces moved distances. - Now apply muscular force to the long end of the lever.. - This rule clarifies the principle of the screw's action. - problem consists in finding the point of application (line of action) of the resultant force.. - We are looking for the line of action of the resultant force F. - The stronger person should take hold of the pole nearer to the load.. - The point of application of the resultant force is called the centre of gravity. - A median divides each of the strips in half. - the pails turn out to be on the level of the tightrope. - We know the result of the computation for two bodies.. - the angular momentum is proportional to the square of the distance from the axis.. - Acrobats make good use of the law of conservation of angular momentum. - The force of the push creates a forward motion, and the torque causes. - This is the mechanics of the somer- sault.. - Two nearby positions of the point are depicted in Figure 5.14. - recall that their magnitudes are proportional to the square of the rotational speed. - Denote the displacement of the shaft by l.. - The flexibility of the shaft is by no means a drawback;. - the second body attracts the first with the force proportional to the mass of the first body.. - We should take the distance from the centre of the Earth to the body as r,. - Let M be the mass, and R the radius of the Earth.. - form of the Earth is "set". - its cause must be rooted in the construction of the Earth's shell.