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I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward. This is wrong. What troubles me here, is the fact that it is traveling through space-time ...

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The answers above are all correct as far as they go, but the next step is even more stunning. If I am A, the object at rest, then I am moving through spacetime at the speed of light. My friend B gets on a spaceship and rockets away at a high constant velocity and to me his time appears to slow down because of his velocity through space. But if my fried B ...

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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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