A uniform block of granite in the shape of a book has face dimensions of 20 cm and 15 cm and a thickness of 1.2 cm. The density (mass per unit volume) of granite is 2.64 g/cm3. The block rotates around an axis that is perpendicular to its face and halfway between its center and a corner. Its angular momentum about that axis is 0.104 kg.m2/s. What is its rotational kinetic energy about that axis?
Angular kinetic energy is 0.62 J.
Using the volume and density, find mass. Find the distance from the axis of rotation using the given information. Using the parallel axis theorem, find the rotational inertia of the system. And finally, find the rotational kinetic energy.
Formula is as follow:
Where, L is angular momentum and I is moment of inertia.
Now, distance from center to point about which block spins is given by,
Rotational inertia of block about axis is,
Now, M.I. about axis of spin is given by parallel axis theorem,
Hence, angular kinetic energy is 0.62 J.
Therefore, the kinetic energy of rotation can be found using the formula of the energy.
Question: A car has four wheels. When the car is moving, what fraction of its total kinetic energy is due to rotation of the wheels about their axles? Assume that the wheels have the same rotational inertia as uniform disks of the same mass and size. Why do you not need to know the radius of the wheels?
A plum is located at coordinates (-2.0M, 0,4.0M). In unit- vector notation, what is the torque about the origin on the plum if that torque is due to a force . (a) Whose only component is role="math" localid="1661237442203" ? (b)Whose only component is ? (c)Whose only component is ? (d) Whose only component is ?
Figure shows a rigid structure consisting of a circular hoop of radius and mass , and a square made of four thin bars, each of length and mass . The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of . Assuming and role="math" localid="1660971946053" ,
(a) Calculate the structure’s rotational inertia about the axis of rotation?
(b) Calculate its angular momentum about that axis?
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