A cylinder of length L is resting at the base of a surface inclined at an angle

Question

A cylinder of length L is resting at the base of a surface inclined at an angle alpha above the horizontal. The cylinder, with mass Mc and radius Rc, is free to rotate about an axis through its center. The coefficient of kinetic friction between the block and the surface is Fm. Block B, with mass Mb, is suspended in air a distance d above the ground. Block B is connected to the axis running through the cylinder by a light, stretchless string passing (parallel to the first surface) over a frictionless pulley of mass Mp and Radius Rp. The string does not slip over the rim of the pulley. A) Use newton

Explanation / Answer

A uniform circular mot ion can be viewed as the combination of two perpendicular simple harmonic motion simultaneously acting on a single plane . For example you can consider that one is along the y axis and another along the x axis . Thus the centripetal acceleration is resolved into two components one along the x axis and another along the y axis . Now consider the motion along the x axis . The object ( say ) starts from the left end of the x axis . It passes through the center and then reaches the other extreme point . It oscillates between the two points every time crossing the center ( center of the circle ) Similarly, this happens along the y axis . It crosses the center of the circle during each oscillation . ===================== Thus in circular motion , one component of the the centripetal acceleration , pulls the object toward the center while the other component pulls it out of the center . That is why it is in circular motion . Imagine what will happen if one of the simple harmonic motion is not present there . The object will oscillate about the center . When the two simple harmonic motions are present simultaneously , the motion is a circle. ( the phase difference between these two motions are of course 90 degree) ================================= Another way of reasoning is to remember that the velocity of the object is always perpendicular to the centripetal force . While the object moves along the radius by a small distance due to the force , the object moves along an arc of a circle . Thus it moves toward the center at every instant , but never reaches the center . ======================================… Note the mistakes in the other answers. If the centripetal force cancels the centripetal force , then the net force is zero and the object cannot move in a circular path.

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