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1

I'm assuming the seesaw is tilted to the left, but not moving. Given a frictionless pivot, if the seesaw is tilted to the left but not moving, then there must be another 10 N force on the right so that the sum of the moments about the pivot is zero. As such, the seesaw is already in balance, albeit not necessarily level (horizontal). It is similar to the ...

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The moment of inertia of any compound object made up of $N$ discrete masses is given by $$I = \sum_{i=1}^{N} m_{i} r_{i}^{2}$$ where $m_{i}$ is the mass of the $i$th object and $r_{i}$ is the distance of the object of the $i$th mass from the axis of rotation. Now, for a continuous object, the summation becomes and integral as in Puk's response. Now in ...

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In general, the moment of inertia is found by evaluating $$I = \iiint\limits_V{\rho r^2 dV},$$ where $\rho$ is the mass density and $r$ is the distance from the axis with respect to which you wish to calculate the moment of inertia (often the axis of symmetry). For complex objects, there usually will not be a simple formula for the moment of inertia and it ...

46

Is it inertia that a rotating object will rotate forever without external force? Someone told me that this is not inertia [...] Well, sort of - it’s somewhat correct to say it is inertia, and somewhat correct to say it isn’t. One has to be precise with language! But there is some truth to what you were told. “Inertia” generally refers to the tendency of ...

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At its most basic, an object will rotate forever for the simple reason that there is no preferred direction in space. Emmy Noether's theorem of 1918 explains how various conservation laws arise from from differentiable symmetries. It is a mathematical theorem, not a physics theory. Because of this mathematical certainty, it is one of the most important ...

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As Newton stated with his 1st law, an object without a force acting on it will keep moving with the same speed and direction. This is also known as the law of inertia. Inertia is the tendency of an object to resist acceleration. This is because no force is acting on it to affect acceleration. For rotational motion, the version of this is the moment of ...

1

Translational equilibrium means that the center of mass of an object feels no force to accelerate it to some direction. The rotational equilibrium means that an object didn't rotate. Both of them are fulfilled for every fixed, non-moving thing. For example, a properly built house will neither give way under it, nor will fall down by rotation. Reactive ...

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But the reaction force is not a force acting on the body, it's a force being exerted by the body. By Newton's third law if the body is exerting a force onto "something" then a force equal in magnitude and opposite in direction is being exerted onto the body by the "something" For example, think of a car on the ground. The car pushes into the ground, so the ...

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The reaction force is just the force according to Newton's 3rd law, it should have the opposite sign to the force that causes the reaction. The reaction force can be caused by linear inertia, moment of inertia (rotational inertia) or another object. Since there is only one object on your diagram - it is the former. The reaction force caused by inertia is a ...

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There is an azimuthal symmetry in the probem, i.e. the force/torque is the same no matter the specific value of $\phi$. Hence, you can choose $\phi = 0$ with no loss of generality.

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as pushing from near the axle. The handle and door are a system acted on by an external force near the axle. As the rod and door are assumed to be rigid the situation is no different to having the space between the rod and the door filled with a rigid material ie having a much thicker door.

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The problem here is that your system is not a rigid body. We can think of it as a point particle (the Earth) rotating about another point particle (the Sun). The system is not rigid because the distance between these two point particles changes over time. Therefore, we need to be more careful with how we apply these rotational analogs of Newton's laws. ...

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