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Magnetic Boots Two astronauts are installing equipment on an orbiting platform that is rotating freely at a rate of 1.10 rad/s about its centre of mass, as shown in Figure 8-53. Astronaut Valentine is standing at the centre of the platform, and astronaut Alexander is at the edge. The platform has a radius of 11.0 m. The moment of inertia of the platform without the astronauts is I_P=2400.kg•m^2. Astronaut Valentine walks to the edge and hands a container of mass m_c=24.0 kg to astronaut Alexander and then returns to the centre. Both astronauts are wearing magnetic boots that keep them on the surface of the platform. Compared to the dimensions of the platform, you can consider the astronauts to be thin cylinders or point masses of mass m_a=81.0 kg each. The container can also be considered a point mass. Find the resulting angular speed of the platform after astronaut Valentine has returned to the centre. Find the total work done by the astronaut(s) in the process. If astronaut V
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Rotation of earth (a) Determine the values for the linear speed, angular speed, tangential acceleration, and radial acceleration of a point at the equator. Assume that Earth is a sphere of radius 6340 km. (b) Calculate how far the rotation of Earth moves a person sitting on a beach at the equator during a 2.00 h sunbath.
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Electronic Engineering
Bicycle Wheel Spin A bicycle wheel spins about its axis at an angular speed of 6.50 rad/s and slows down because of friction with an acceleration of 8.20 〖rad/s〗^2. Find the time it takes the wheel to reach a speed of 3.20 rad/s.
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Spinning Flywheel A flywheel of radius 0.720 m is rotating clockwise at 3.60 rad/s. Find the acceleration needed to slow the wheel to an angular speed of 2.10 rad/s over 1.80 s. Assume the acceleration is constant. Find the number of revolutions the wheel will go through as it slows down.
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Supporting a Beam The beam in Figure 8-15 is supported by a free hinge at the pivot. If left under the effect of the force of gravity, it would swing down freely. You wish to prevent it from doing so. The beam at the instant shown makes an angle of 20.0° with the vertical and you are applying your force of 98.0 N horizontally. If the top of the beam is 1.60 m above the pivot vertically, what is the torque applied by your force? Calculate the moment arm for the applied force, and use the moment arm to calculate the torque as well.
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Laptop Glare Your laptop screen sits in the yz-plane (vertical). You wish to push it back a little by exerting a force in the horizontal direction at the top of the screen so you can read better. (The force you exert is in the negative x-direction). Establish the direction of the torque about the rotation axis (or pivot) at the bottom of the screen, and express the torque in vector form. The screen’s height is l and its width is w.
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Clever Monkey The solid drum in Figure 8-36(a) is free to rotate about an axis through its centre. A 23.0 kg monkey decides to ride the rope on the drum down to the ground 12.0 m below. The rope is at rest when the monkey grabs onto it. The drum is a uniform cylindrical disk of radius 0.180 m and mass 190.0 kg. Find the acceleration of the monkey and the tension in the rope. Assume that the mass of the rope is negligible.
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Moment of inertia for a combination of Objects As shown in Figure 8-37, a uniform disk is of radius R and mass m1. Attached to the disk is a thin ring of mass m2 and radius R. There is a small mass m3 (assume a point mass) attached to the surface of the disk at a distance of R/2 from the rotation axis through the centre of the disk perpendicular to the plane of the disk. The direction of rotation is shown in the figure for added clarity. What is the moment of inertia of the composite object?
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Electronic Engineering
