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A merry-go-round with a moment of inertia equal to1260 $\mathrm{kg} \cdot \mathrm{m}^{2}$ and a radius of 2.5 $\mathrm{m}$ rotates with negligiblefriction at 1.70 $\mathrm{rad} / \mathrm{s} .$ A child initially standing still next tothe merry-go-round jumps onto the edge of the platform straight toward the axis of rotation causing the platform to slow to 1.25 rad/s. What is her mass?
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Physics 101 Mechanics
Chapter 11
Angular Momentum; General Rotation
Moment, Impulse, and Collisions
Rotation of Rigid Bodies
Dynamics of Rotational Motion
Equilibrium and Elasticity
Rutgers, The State University of New Jersey
University of Michigan - Ann Arbor
University of Winnipeg
Lectures
02:21
In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.
04:12
In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.
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A 3.0 -m-diameter merry-go…
angular momentum is conserved in the interaction between the child on the merry go round because there is no external dark. Therefore, l I mystical toe and left where I stands for initial and F stands for final. Therefore l i e off the child was ally off, though maybe go down Mrs. Acquittal left off the tide less lf off America And since the child is at rest Initially I thought this ghost recede o no angular momentum off angular momentum is given by I times Omega Therefore, for the merry go round, this will be quality Hi. Off the merry go round times omega off the merry go round initially which is Omega not And this is equal Do on f c plus l f m on lfc is moment of finish off the child Thanks, amigo That only guys the final limit off inertia after its little stone. After the medical down slows down on dde Also left m will be called toe. I am Science Omega Since they bought since the tile is on the merry go round, they slow down and they have the same angular velocity. So we take the final angular velocity out off the expression. So this is what be God Now the moment of inertia off the child is just a mar scratch and our is the radius off the medical around because it said this system, Acheron and Giant is sitting on the on the circumference off the circle. Therefore from the center, it's just insists on. And since woman off inertia is taken about the access therefore a moment of inertia off the child will be called the mass of the child dying Spare off this radius. So we like that over here now from this expression began solved for the most off the chain which will be equal toe I am times only got not minus omega. Basically, the difference between the initial and final Angela velocities are square days after me to go around Guys Omega. Now, given these values, we can solve this expression now and we get the mass off the child to the equal. Do 70 Chikage is
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