11. A cylinder having a mass of 8.0 kg can rotate about its central axis through
ID: 1264424 • Letter: 1
Question
11.
A cylinder having a mass of 8.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 6.5 N, F2 = 5.0 N, F3 = 2.0 N, and F4 = 6.0 N. Also, R1 = 6.0 cm and R2 = 11.0 cm. Find the magnitude and direction of the angular acceleration of the cylinder.(Take clockwise to be +) (During the rotation, the forces maintain their same angles relative to the cylinder.)
A cylinder having a mass of 8.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 6.5 N, F2 = 5.0 N, F3 = 2.0 N, and F4 = 6.0 N. Also, R1 = 6.0 cm and R2 = 11.0 cm. Find the magnitude and direction of the angular acceleration of the cylinder.(Take clockwise to be +) (During the rotation, the forces maintain their same angles relative to the cylinder.)Explanation / Answer
Given that mass of the cyllinder is m = 8.0 kg
??_net = I ?
moment of inertia I = 1/2 M R_2^2
= 1/2 * 8.0 kg * ( 0.11 m)^2
= 0.0484 kg m^2
? ? = F_1 R_2 - F_2 R_2 -F_3 R_1 * F_4 * 0
= 6.5 N * 0.11 m - 5.0 N * 0.11 m - 2.0N * 0.06 m
= 0.045 N m
angular acceleration ? = ? ? / I
= 0.045 N m / 0.0484 kg m^2
= 0.9297 rad /s^2
direction of angular accelaration is clockwise (positive)
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