A round object has a mass m , radius R , and a rotational inertia I = NmR 2 . It

Question

A round object has a mass m, radius R, and a rotational inertia I = NmR2. It starts at rest at a height h on an inclined plane, then rolls down the hill. Determine a symbolic expression for v, the speed of this object when it reaches the bottom of the hill. Then enter your symbolic answer as a function of m, R, N, g, and/or h in Excel notation. Upper- and lower- case matter! Other numeric constants, such as 1.0, or 0.5 are also permitted, but be sure to include a decimal point in every numeric constant. As with all symbolic answers, do not include any units or unit conversion factors.

Explanation / Answer

as the body slides down its potential energy decrease and kinetic energy increases.

m*g*h = 0.5*m*v^2 + 0.5*I*w^2

= 0.5*m*v^2 + 0.5*N*m*R^2*w^2

m*g*h= 0.5*m*v^2 + 0.5*N*m*v^2

g*h = v^2(0.5 + N*0.5)

v = sqrt( g*h/(0.5+0.5*N) )

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