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Derive the relation
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Vector Mechanics For Engineers
- As shown in the picture below, a 40-kg diver is positioned so that his radius of gyration is 0.4m as he leaves the board with an angular velocity of 5 rad/s (Position 1). What is the diver's angular velocity when he changes his pose to Position2, altering his radius of gyration to 0.2m? Position 1 Position 2 CARarrow_forward3. A thin piece of metal of mass 80 g has the cross section shown in Fig. 17. Find the moment and products of inertia for the axes Ox and Oy. Through what angles must these axes be rotated to coincide with the principal axes? Suppose the body is rotating at a given instant about the Ox axis with an angular velocityarrow_forwardA point charge q1 = +5.00 micro Coulomb is held fixed in space. From a horizontal distance of 6.00 cm, a small sphere with mass 4.00 x 10-3 kg and charge q2 = +2.00 micro Coulomb is fired toward the fixed charge with an initial speed of 40.0 m/s. Gravity can be neglected. What is the acceleration (in m/s2) of the sphere at the instant when its speed is 25.0 m/s?arrow_forward
- In his mission as a spy, Loid Forger fired a bullet weighing mB = 0.007 kg with a horizontal speed of VB= 550 m/s into the lower end of a gate which can be modeled into a slender m=16-kg bar of length L=1.5m for simplified analysis only. Know that h=0.25 m and that the gate, which has a pin connection at point C, is initially at rest. The bullet becomes embedded into the gate after impact. 1.5 m с A D 0.25 m VB= 550 m/sarrow_forwardWhat is conservation of angular momentum?arrow_forwardA 100 kg vehicle initially travels clockwise in a circular path with a radius of 10 m at a speed of 5 m/s. If a counterclockwise couple moment of 100 Nm is applied for 10 s, and the vehicle continues to travel on a circular path at 5 m/s, then the circular path radius must drop to from 10 m to 8 m. True Falsearrow_forward
- Angular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…arrow_forward[Level 1] A 100 g marble is constrained to move in a circular path on a frictionless horizontal surface under the action of an electromagnetic force that varies according to Fe(t) = 2e0.1t N and is tangent to the path. The radius of the path is R = 0.75 m. Find how fast the marble is spinning about the center O after 2 s if it starts from rest. ter `R Top view E3.5.11arrow_forwardAngular Impulse and Momentum Principles To apply the principle of angular impulse and momentum to describe a particle's motion. The moment of a force about a point O, fixed in an inertial coordinate system, MO, and the angular momentum about the same point, HO, are related as follows: ∑MO=H˙O where H˙O is the time derivative of the angular momentum, HO=r×mv. Integrating this equation with respect to time yields the following equation: ∑∫t2t1MO dt=(HO)2−(HO)1 This equation is the principle of angular impulse and momentum, and it is often rearranged to its more familiar form (HO)1+∑∫t2t1MO dt=(HO)2 A centrifugal governor consists of a central rotating shaft that has two thin, pin-connected rods attached to it; a heavy sphere caps the end of each rod. (Figure 1) A centrifugal governor mechanically limits an engine's speed. A part of the engine turns the centrifugal governor, and if the speed exceeds a set amount, the height of the spheres decreases the driving force of the engine by…arrow_forward
- Question 19: A particle of mass m coming with velocity Vo hits the center of mass of a uniform rod of mass M and length L on a horizontal frictionless table as shown in Figure 11. The collision is completely inelastic. The rod is pivoted at point P, the left end. The moment of inertia of the rod about the pivot is Ip =ML². Find the angular velocity of the system after the collision. М, L P L/2 Vo Figure 11 Select one: 6mvo (4М + 3т)е 6mvo (ЗМ + 4m)е 12mvo (4М + Зт)е mvo (M +3m)l 12mvo (ЗМ + 4т)еarrow_forwardb. Find the equation of motion of the system below using Lagrange's equation. Masses m₁, m2, and m3 are added to the compound pendulums with rod masses Mr₁, Mr2, and Mr31 respectively. Assume the mass of all pendulums are evenly distributed so that their center of gravity is in the middle of the pendulum of length L. Use the small angle assumption. O ○ L 02 M1 L m3 m2arrow_forwardChannel AB is fixed in space, and its centerline lies in the xy plane. The plane containing edges AC and AD of the channel is parallel to the xz plane. The surfaces of the channel are frictionless and the sphere E has 1.9 kg mass. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. N N E 30° x F 20° B ᎠᏓ C 30°/A 30° Determine the force supported by cord EF, and the reactions RC and RD between the sphere and sides C and D, respectively, of the channel. (Round the final answers to four decimal places.) The force supported by cord EF is The reactions RC and Rp between the sphere and sides Cand D. respectively, of the channel are as follows: RC= RD= z N. 4arrow_forward
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