Given 10 cc of lead, find how to form it into a solid of revolution of height 1 cm and minimum moment of inertia about its axis.
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Given 10 cc of lead, find how to form it into a solid of revolution of height 1 cm and minimum moment of inertia about its axis.
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- A solid, horizontal cylinder of mass 15.0 kg and radius 1.00 m rotates with an angular speed of 6.00 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.A solid sphere of mass M and radius R rolls without slipping down a rough incline that makes an angle θ with the horizontal. Find the magnitude of the linear acceleration a of the sphere.A uniform thin spherical shell of mass M-2kg and radius R=0.45m is given an initial angular speed w=11rad/s when it is at the bottom of an inclined plane of height h=3.7m, as shown in the figure. The spherical shell rolls without slipping. Find w if the shell comes to rest at the top of the inclined plane. (Take g=9.81 m/s2, Ispherical shell = 2/3 MR2 ).Express your answer using one decimal place. h M, R
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- Two circular cylinders have the same mass and dimensions, but one is solid while the other is a thin hollow shell. If they are released together to roll without slipping down the plane, inclined at 30° to the horizontal, how far apart will they be after 10 seconds? mg sin 30 ng cos 30 30 mgThe uniform thin rod in the figure below has mass M = 2.50 kg and length L = 2.87 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end. HINT L/2 × CG M O (a) the rod's angular acceleration (in rad/s²) rad/s² (b) the tangential acceleration of the rod's center of mass (in m/s²) (c) m/s² the tangential acceleration of the rod's free end (in m/s²) m/s²The spool has a mass, m, and a radius of gyration, kG. An inextensible is wrapped around the inner diameter of the spool and is attached to the wall a point A. The coefficient of friction between the floor and the spool is mu. If the spool has the initial angular velocity given as omega naught, how far will the center, G, move before stopping?