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$\bullet$ (a) In each of the objects indicated in Figure $10.56,$ what magnitude of force $F($ if any) is needed to put the object into rotational equilibrium about the axis $A$ shown? (b) After you have found the $F$ required to put the object into rotational equilibrium, find out which (if any) of these objects is also in translational equilibrium.

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a) 150 $\mathrm{N}$b) $ 16,67 \mathrm{N}$c) 230 $\mathrm{N}$d) 16.67 $\mathrm{N}$e) $O \mathrm{N}$

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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Lectures

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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The object shown in Fig. 9…

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shows two forces acting on…

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Determine the magnitude of…

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Determine the torques abou…

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Three Force The body in Fi…

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Each of the objects in Fig…

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$\bullet$ In Figure $10.44…

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An object is subjected to …

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$\cdot$ Which of the objec…

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A particle is acted on by …

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10:57

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Pivoted at $O$ The body in…

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Find the magnitude, direct…

so here rotational equilibrium is defined as thie network equaling zero Translational equilibrium is defined as the sum of the forces equaling zero. So for part A, we have rotational equilibrium. The Sigma Tau, or the son of the torques, equal zero. And we can say that 50 Newtons times 30 centimetres equals the force times 10 centimeters. Here the force is going to be equal to 150 Newton's. And because the 150 noons is not equal to 50 Newton's, that means that there is ah, no translational equilibrium, So not in translational equilibrium. Now, for part B, they're asking us again. Sigma Tau equals zero. This produces 50 Nunes times 10 centimeters. This equals the force times 30 centimeters. And in this case, the force now equals 16.67 noons. And against 16.67 noons is not equal 50 Nunes. So this is also not in translational equilibrium. And you have to do this for all the cases up until case e So for see again Sigma Tau equals zero and we have 50 newtons times 30 centimeters plus 40 nunes times 2017 years. So we can already we already know that this is not in translation alike. A librium. Um, this C on this equals f times 10 centimeters, so we know that half is going to be equal. Tow 230 Nunes manic and not in translational equilibrium. It's the sum of the forces. Do not equal zero report D we have again. Sigma Tau equals zero and we have 50 nunes times 10 centimeters. This is equaling force times 30 centimeters. So again, force equals 16.67 Nunes. And this is not in translational equilibrium either. And for the last case, case E Sigma Tau equals zero. And again we have 100 nunes times 15 centimeters. This equals 50 Newtons times 30 centimeters plus f times 10 centimeters. And we're finding out that f equals zero Newtons. But again, this's not in translational equilibrium because 50 Nunes does not cancel out 101 100 Newton's so not in. So none of the cases Aaron, transistor, translational equilibrium and all of the cases are in rotational equilibrium. That is how we're able tto find what the magnitude of the force is. That is the end of the solution. Thank you for watching

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