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Q: 500 N 2 m
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- A 2.00 kg rock has ahorizontal velocity of magnitude12.0 m/s when it is at point P inFig. . (a) At this instant, whatare the magnitude and direction of itsangular momentum relative to pointO? (b) If the only force acting on therock is its weight, what is the rate ofchange (magnitude and direction) ofits angular momentum at this instant?Four objects are situated along the y axis as follows: a 1.98-kg object is at +2.94 m, a 3.08-kg object is at +2.49 m, a 2.43-kg object is at the origin, and a 3.99-kg obgect is at -0.496m where is the center of mas of these objects? Need Help? Read It Watch t A rod of length 34.50 cm has linear density (mass per length) given by 1= 50.0 + 22.Dx where x is the distance from one end, and i is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass?Look for the center of mass of a uniform solid right circular cone using M as mass, R as radius and H as Height.
- Compute the combined moment of the two 70-lb forces about (a) point O and (b) point A. The moment is positive if counterclockwise, negative if clockwise. Assume a = 4.7 in., b = 2.8 in., F = 70 lb. y Answers: (a) Moi (b) MA i O lb-in. lb-in.9.30 Four small spheres, eachof which you can regard as a pointof mass 0.200 kg, are arranged ina square 0.400 m on a side andconnected by extremely light rods Find the momentof inertia of the system about anaxis (a) through the center of thesquare, perpendicular to its plane(an axis through point O in the figure); (b) bisecting two oppositesides of the square (an axis along the line AB in the figure); (c) thatpasses through the centers of the upper left and lower right spheres andthrough point O.In ice figure skating, a couple execute a“top” (see picture). The centre of mass ofthe woman (58 kg) is situated 1.3 m fromthe axis of rotation which is vertical andpasses through the centre of mass of theman (85 kg). They are spinning at aconstant angular velocity equal to ?? rad/sand the man and woman have moments ofinertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity.Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine...the axis they’re rotating about passes through his CoM, but the…
- A box weighing 25 pounds (assumed concentratedat its center of gravity) is being pulled by a horizontalforce F equal to 20 pounds. What is the moment aboutpoint A? Does the box tip over?The tennis racket of the previous question is modified by adding a point mass m, = m/2 to the part of the rim furthest from the shaft. Find the new posi- tion of the center of mass.The moment of inertia of thehuman body about an axis through its center of mass is importantin the application of biomechanics to sports such as diving and gymnastics. We can measure thebody’s moment of inertia in aparticular position while a personremains in that position on ahorizontal turntable, with the body’scenter of mass on the turntable’s rotationalaxis. The turntable with theperson on it is then accelerated fromrest by a torque that is produced byusing a rope wound around a pulleyon the shaft of the turntable. Fromthe measured tension in the rope andthe angular acceleration, we can calculatethe body’s moment of inertiaabout an axis through its center of mass.The moment of inertia of the empty turntable is 1.5 kg . m2.With a constant torque of 2.5 N . m, the turntable–person system takes3.0 s to spin from rest to an angular speed of 1.0 rad/s. What is theperson’s moment of inertia about an axis through her center of mass?Ignore friction in the turntable axle. (a) 2.5 kg . m2;…
- The moment of inertia of thehuman body about an axis through its center of mass is importantin the application of biomechanics to sports such as diving and gymnastics. We can measure thebody’s moment of inertia in aparticular position while a personremains in that position on ahorizontal turntable, with the body’scenter of mass on the turntable’s rotationalaxis. The turntable with theperson on it is then accelerated fromrest by a torque that is produced byusing a rope wound around a pulleyon the shaft of the turntable. Fromthe measured tension in the rope andthe angular acceleration, we can calculatethe body’s moment of inertiaabout an axis through its center of mass.If the body’s center of mass were not placed on the rotational axis of the turntable, how would the person’s measured moment of inertia compare to the moment of inertia for rotation about the center of mass? (a) The measured moment of inertia would be too large; (b) the measured moment of inertia would be too small; (c)…The moment of inertia of thehuman body about an axis through its center of mass is importantin the application of biomechanics to sports such as diving and gymnastics. We can measure thebody’s moment of inertia in aparticular position while a personremains in that position on ahorizontal turntable, with the body’scenter of mass on the turntable’s rotationalaxis. The turntable with theperson on it is then accelerated fromrest by a torque that is produced byusing a rope wound around a pulleyon the shaft of the turntable. Fromthe measured tension in the rope andthe angular acceleration, we can calculatethe body’s moment of inertiaabout an axis through its center of mass.While the turntable is being accelerated, the person suddenly extends her legs. What happens to the turntable? (a) It suddenly speeds up; (b) it rotates with constant speed; (c) its acceleration decreases; (d) it suddenly stops rotating.4.30P ) a) A piece of gum of mass ml is thrown at a bar of mass m2 and length of d, pivoted about its center and initially at rest as shown in figure. The gum sticks to the end of bar and the final angular speed of the bar is measured to be w. What is the vi initial speed of the gum? b) Calculate the moment of inertias of systems in figures. Each of mass is m and distance between them is 2d. Rotation axes are shown in figure.