For Problems 2 to 6, given
Let A and C be drawn from a common origin and let C rotate about A with an angular velocity of 2 rad/sec. Find the velocity of the head of
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- Gear Trains Figure 8 shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n1 and the second gear has n2 teeth. Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If 1 and 2 are the angular velocities of the first and second gears, respectively, then v2=v1r22=r112=r1r212=n1n21 The second gear in a single-stage gear train has 6 teeth and an angular velocity of 90 revolutions per minute. The first gear has 54 teeth. Find the angular velocity of the first gear.arrow_forwardA hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 13 feet. The ball is started in motion from the equilibrium position with a downward velocity of 4 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second per second.arrow_forwardThe motion of a vibrating particle is defined by the position vector r = (4 sin nt)i – (cos 2ntj, where ris expressed in inches and tin seconds. (a) Determine the velocity and acceleration when t= 1 s. (b) Show that the path of the particle is parabolic. Fig. P11.91 1 in. 11 in.arrow_forward
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