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A playground merry-go-round has a radius of 4.40 $\mathrm{m}$ and a moment of inertia of 245 $\mathrm{kg} \cdot \mathrm{m}^{2}$ and turns with negligible friction about a vertical axle through its center. (a) A child applies a 25.0 $\mathrm{N}$ force tangentially to the edge of the merry-go-round for 20.0 s. If the merry-go-round is initially at rest, what is its angular velocity after this 20.0 s interval? (b) How much work did the child do on the merry-go-round? (c) What is the average power supplied by the child?

a) 8.98 $\mathrm{rad} / \mathrm{s}$b) $9.88 \times 10^{3} \mathrm{J}$c) 494 $\mathrm{W}$

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

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02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

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.

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A playground merry-go-roun…

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for problem. 19. We have a married girl around. Yes, that's a radius of 4.4 meters with a moment of inertia As 245 Look around you. You're squared. Um, and we noting that the child is applying the force on the merry go round of 25 Newtons. A couple of questions. First off, they want to know if, um, this merry go round was initially at rest and, um, 20 seconds past. What would our final velocity B fun, angular velocity using some of our kin O Matic formulas we know we could solve for a final angular velocity if we know are angular acceleration? That's where force comes in. We know that this child not only applied force but applied a tour to that merry go round. Torque is defined as with torches to find as moment of inertia times angular acceleration. Our torque is R force times, our liver on which in this case is 25 times our radius of 4.4. That's equal to our moment of inertia to 45 and times angular for loss or angular acceleration. Been suffering the acceleration get 0.45 radiance per second squared subbing in here We know it starts at rest. 0.45 20 seconds gives us a final angular velocity of 8.9 radiance per second. And that's party. Part B then asks for how much work did the child doing the merry go round and see asks for the power supplied by this child. So part B. We know that work is fine as torque times are angular displacement. Now going back to cinematics, we're gonna have to go back to automatics and find out what angular displacement we had during this time interval. So knowing our aromatics formulas we know we can sell for angular displacement is initial angular velocity. It's time. 1/2 angular acceleration times squared course initially were zero. Subbing in during the 20 seconds gives us an angular displacement with 89.8, so that then, knowing our torque is forced, 25 mittens live around 4.4 8.9 gives us a work or 98 78 Jules, Finally, sea power power is the find work overtime. We just calculated our work to be 98 78 and we know that occurred in that 22nd time interval gives us 4 94 watts of power. Thank you for

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