The 2-kg heavy pinion gear is at rest when a force F U = 10N to the left is appl

Question

The 2-kg heavy pinion gear is at rest when a force FU= 10N to the left is applied to the 2-kg heavy upper rack and a FL=10N to the right is applied to the 3-kg heavy lower rack. Determine the angular velocity of the gear after 3s of motion using methods involving impulse and momentum.

The 2-kg heavy pinion gear is at rest when a force FU= 10N to the left is applied to the 2-kg heavy upper rack and a FL=10N to the right is applied to the 3-kg heavy lower rack. Determine the angular velocity of the gear after 3s of motion using methods involving impulse and momentum.

Explanation / Answer

Upper rack acceleration = 5m/s2

Lower rack acceleration = 3.33 m/s2

Impulse due to upper rack = 10*3 =30N-s

Impulse due to lower rack = 30N-s

Total impulse = 60N-s

Angular momentum of pinion = (mr*r/2)*w

This is equal to the torque produced by impulse = 60*0.3 = 18J-sec

From this, angular velocity w = 2*18/(2*0.3*0.3) = 200rad/sec

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