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For me the second case was more intuitive. The friction and gravity both induce torques of the same sign on the body. Gravity acts through the center of mass, which in this case aligns with the center of rotation. So gravity is not inducing any torque. All the torque is coming from friction. If you imagine the same scenario where the ramp is ...

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Friction always opposes relative motion of the point of contact. To know the direction of friction assume that no friction is present and see the direction in which point of contact is moving: friction is opposite to that direction .

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There is no extra energy - the blueshift is due to an increase in the observed frequency, not the actual frequency. The light is still being emitted at the same frequency so the same amount of energy is used.

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While people normally quote Newton's Second law as $\vec F = m \vec a$, it is better written as $$\vec F = \frac{d\vec p}{dt}$$ Force is a rate of change in momentum. This means that the average force applied when an object undergoes some discrete change in its momentum is $$F_{\text{avg}} = \frac{\Delta p }{\Delta t}$$ The change in your momentum ...

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