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describe the mathematical steps necessary to write the exponential decay equation for the voltage across a capacitor in an RC circuit as a linear equation with independent variables x=ln(ε/V) and y=t.
<p>Consider a lollipop made of a solid sphere of mass m andradius r that is radially pierced by a massless stick. The free endof the stick is pivoted on the ground, which is frictionless. Thesphere slides along the ground, with the same point on the spherealways touching the ground. The center moves in a circle of radiusR with frequency Ω. Show that the normal force between theground and the sphere is N=mg + mrΩ^2, which isindependent of R. Solve this by:</p><p>a) Using an F=ma argument.</p><p>b) Using the more complicated torque = dL/dtargument.</p>