Question

A uniform cylinder of radius 11 cm and mass 24 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 4.6 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

Answer 1

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A uniform cylinder of radius 40 cm and mass 22 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 55.0 cm from the central longitudinal axis of the cylinder.
(a) What is the rotational inertia of the cylinder about the axis of rotation?
(b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

solution:

A uniform cyllinder radius R = 40 cm

mass of the cyllinder is M = 22 kg

height is h = 55.0 cm

a ) Rotational inertia of the cyllinder about the axis of the rotation is

I = I_com + Mh^2

= 1/2 MR^2 + Mh^2

= 1/2 * 22 kg ( 40*10^-2 m)^2 + 22 kg ( 55 *10^-2 m)^2

= 8.41 kg m^2

b ) the angular speed of the cylinder as it passes through its lowest position is

? = ? 2 * Mg h / I

= ? 2 * 22 kg * 9.8* 55*10^-2 m / 8.41 kg m^2

= 5.30 rad /s

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