Consider a disc of mass 0.44kg, with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc. What is the moment of inertia for the disc rotating around its central axis?
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Consider a disc of mass 0.44kg, with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc.
What is the moment of inertia for the disc rotating around its central axis?
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- A homogeneous pulley with two grooves consists of two wheels which turn together as one around the same axis. The moment of inertia of the two wheels together is ICM = 40 kg m2. The radii are: R1 = 1.2 m and R2 = 0.4 m. The masses that hang on both sides of the pulley are m1 = 36 kg and m2 = 12 kg. We will assume that the masses of the ropes are negligible. Determine the angular acceleration of the pulley, acceleration of the masses, and the tensions of the ropes.A uniform disk of mass 7 kg and radius 0.2 m is free to rotated about an axis perpendicular to its center. A constant force of size 146 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 169 full rotations. What is the angular momentum of the disk after those rotations are complete, in kg m2/s? It could be useful to you to know that the rotational inertia of a uniform disk is 1/2 M R2. (Please answer to the fourth decimal place - i.e 14.3225)A student sits on a pivoted stool holding a pair of weights. The stool is free to rotate about vertical axes with negligible friction. The student is set in rotation with arms outstretched, holding a 5-kg mass in each hand. He is rotating about a vertical axis with an angular velocity of one revolution per second, arms outstretched. If he pulls the weights inward, what will the final angular velocity (in rev/s) be if his moment of inertia remains approximately constant at 5 kg×m2, and the distance of the masses from the axis changes from 1 m to 0.1 m?
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- You are trying to get a better feel for the effect of geometry and mass distribution on the moment of inertia. You have a solid disk and a thin ring, each of radius, r = 1.30 m, and mass, m = 73.0 kg. You mount both on fixed, horizontal frictionless axes about which they can spin freely. Then you spin them both. (a) How much work do you need to do to get each object to spin at 3.00 rad/s? (b) Let us assume that you have been causing them to spin by using a constant force applied tangentially to their circumferences. If the above speed is to be reached within 0.700 s, what is the magnitude of the force you need to apply to each object? (c) You next attempt to stop each object by pressing one finger on each side of each object, right at the outer edge. The coefficient of kinetic friction between each finger and the surface of each object is 0.300. Find the minimum force you have to apply to stop each object within 1.00 min.A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.50 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles.(a)What is the moment of inertia of the system in kg · m2? (b)If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have? (c)Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2? (d)If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s?A turntable of radius R=2.00 m and mass M=32.0 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4x rad/s. The fixed turntable bearing is frictionless. The turn table is in the shape of a uniform disc with the moment of inertia of this turntable being I 0.5*MR?. (a) What is the magnitude of angular momentum of this turntable? Answer: 803.84 (b) What is the (magnitude of) the momentum of this turntable? Answer: 401.92 kgm2/s? X kgm/s? Now a lump of clay of mass m=2.48 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to a point 1.90 m from the axis (c) Find the final angular speed of the clay and turntable. Answer: 12.386 X rad/s