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In Figure, a constant horizontal force Fapp of magnitude 12 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 10 kg, its radius is 0.10 m, and the cylinder rolls smoothly on the horizontal surface.
(a) What is the magnitude of the acceleration of the center of mass of the cylinder?
(b) What is the magnitude of the angular acceleration of the cylinder about the center of mass?
(c) In unit-vector notation, what is the frictional force acting on thecylinder?
(a) Prove that
(( x ((2 ( ( x ( v1 (2 + ( x ( v2 (2 + ( ( ( + ( x ( vk (2
(This inequality is called Bassel’s Inequality.)
(b) Prove that Bessel’s Inequality is an equality if and only if x is in span (S).
