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(I) What are the x, y, and z components of the
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- If you know the velocity of a particle, can you say anything about the particle’s angular momentum?arrow_forwardA thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through its center of mass. Find the magnitude of therods angular momentum.arrow_forwardThe mass M and moment of inertia C of a thick shell of uniform density p, with internal radius r and exter- nal radius Rare given by M= mp(R³ – r³) CTp(R$ – r³) 8 15" The Earth has an internal structure consisting of con- centric spherical shells. A simple model with uniform density in each shell is given in the following figure. Radius Density Layer (km) (kg m-3) 6370 upper mantle 3300 -5700 lower mantle 5000 3480 outer core 11000 -1220- inner core 13000 (a) Compute the mass and moment of inertia of each spherical shell. (b) Compute the total mass and total moment of inertia of the Earth. (c) If the moment of inertia can be written C= kMR?, where M is Earth's mass and Rits radius, what is the value of k? (d) What would the value of k be if the density were uniform throughout the Earth?arrow_forward
- Two equal point masses m₁ = m2 = 0.69 kg are attached to the ends of a rod of a negligible mass and length of ().81 m. The rod is placed at rest on the y axis and is free to move in a horizontal and frictionless table, as seen in the figure. m1 m3 νο m2 x A third point mass m3, identical to the two other masses, moves with velocity vo collides head-on with completely inelastically collision with m2. = 1.62 m/s to the right so that at t = () it a. Find the center of mass (XCM, YCM) of the three bodies at t₁ = 1.2 s after the collision: Хом 0.64 = Усм -0.2 X b. What is the magnitude of the angular momentum of the system relative to the origin of coordinates? 0.90 X c. What is the magnitude of the angular momentum of the system relative to the center of mass? 0.60 X d. What is the angular velocity of the rod after the collision? 0.5 X e. What is the linear velocity of the body m₁ right after the collision (relative to the laboratory frame of reference)? 0arrow_forwardthe slender bar of length l and mass m is pinned to verical shaft at O, the vertical shaft rotates with a cnstant angular velocity w0, please find the value of necessary for the bar to remain at a constant angular β relative to the vericalarrow_forward20-43. At the instant 0 = 30°, the frame of the crane is rotating with an angular velocity of wi = 1.5 rad/s and angular acceleration of o = 0.5 rad/s, while the boom AB rotates with an angular velocity of wz = 0.5 rad/s and angular acceleration of on = 0.25 rad/s. Determine the velocity and acceleration of point B at this instant. 1.5 m 12 marrow_forward
- What is the angle between the vectors a = (10, -10, 0) and b = (-5, 5, 2), in radians?arrow_forwardA mouse of mass m jumps on a freely rotating disc of moment of inertia I and radius R. If wo and w are the angular velocities of 4 the disc before and after mouse jumps, then the ratio w/wo is: (a) I/mR? (b) I/I-mR? (c) I/I+mR? (d) (I-mR?)/Iarrow_forwardProblem 3: Rotation axis- Particle A thin rod of length L and mass M rotates at angular speed w anti-clockwise. A downwards particle of mass * and speed vo hits the rod at distance d from the rod's axis and perpendicular to the rod. The particle then sticks onto the rod at its impact point. (a) At what value of d are the rod and particle stationary after the hit? (b) If d is greater than the value found in (a), in which direction do the rod and particle rotate?arrow_forward
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