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The job of the motor torque isn't to resist gravity or the weight of the payload (camera). This job falls onto the motor bearing and the design of the axle. However, the axle is allowed to rotate it is going to need some torque to turn due to friction and the overturning moment created by the camera. Ideally, to minimize this effect, you are going to need to ...

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If the ball is subject only to external forces coming from the floor (plus obviously its weight), it may slow down resulting in a decrease in its kinetic energy only by work done by friction forces and friction torque. Let's now for simplicity consider an ideal case with no rolling resistance, then there can be work done by tangential friction only if the ...

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Here are my thoughts: when you pull up, some lower body twists can make the pull up easier (e.g. swinging your legs gives you extra kinetic energy which you can use to help pull yourself up). The heavy weight attached near your lower body would make such twists harder. Furthermore, even if you did twist, the weight will still stay centered, so the 'cheating' ...

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You kind of have to reject the analogy to understand things deeper. Linear and angular momentum are not two separate things but exist together to describe the overall momentum state of a rigid body. Just as linear and angular velocity exist together describing two qualities of the motion of a body. In fact, force and torque also exist together to describe ...

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Actually, the change is velocity is greater when the torque is applied further away from the centre of rotation. You have considered your rotational inertia (I') to be varying according to r but it is constant for a given body as it is analogous to mass. Since the moment of inertia (I) is a constant and angular velocity is dependent on the point of ...

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As pointed out by others, with good bearings and maybe a counterweight, very little torque would be needed to maintain a constant angular velocity. You need to be concerned about how you will control the speed (with gears, a drive belt, or a variable speed motor).

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What is often missed in such debates, is that a commercial toilet paper suspension usually looks like in the image below. The metal lid on the top actually serves to prevent the roll from rotating, while one is tearing the paper. In absence of such a lid, one has to block the roll either by one's hand/fingures (typically in the over orientation) or against ...

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Understand that there is a tradeoff. You can apply a smaller force with a larger wrench, but you have to move it through a larger distance (arc length) to accomplish the same amount of work (force x distance).

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Intuitively, torque is the amount of "rotational oomph" you can give to something. The principle you mention is the one by how a wrench works: it increases the $r$ from your hand and whatever you're trying to wrench, e.g. a bolt - and thus increases the torque. Or conversely, if we were given a set of wrenches and told to try turning various bolts ...

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The best definition of torque (or moment) is the work per unit angle of rotation (in Joules per radian) that can be done by a force which is acting in a manner that tends to cause a rotation. This implies that you want the component of the force which is acting along an arc, times the arc length, divided by the angle (in radians). But the arc length s = rθ, ...

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