A uniform cylinder of radius 13 cm and mass 15 kg is mounted so as to rotate fre

Question

A uniform cylinder of radius 13 cm and mass 15 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.4 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

Explanation / Answer

(A) Icm = m r^2 /2

= 15 x 0.13^2 /2 = 0.12675 kg m^2

I = Icm + m d^2

I = (0.12675) + (15 x 0.054^2) = 0.17 kg m^2

(B) Applying energy conservation,

PE + KE at initial position = PE + KE at final position

m g h + 0 = m g (-h) + I w^2 / 2

2 m g h = I w^2 /2

2 x 15 x 9.8 x 0.054 = 0.17 w^2 /2

w = 13.65 rad/s

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