Chapter 10, Problem 064 A uniform cylinder of radius 12 cm and mass 21 kg is mou

Question

Chapter 10, Problem 064 A uniform cylinder of radius 12 cm and mass 21 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.8 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? (a) Number | Units | (b) Number Units L

Explanation / Answer

A uniform cyllinder radius   R = 12 cm

mass of the cyllinder is M = 21 kg

height is h = 58 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 * 21 kg ( 12*10^-2 m)^2 + 21 kg ( 58 *10^-2 m)^2

=7.2156 kg m^2

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

                 = 2 * Mg h / I

   2 *21*9.8* 58*10^-2 m/7.2156

=5.75 rad/s

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