(hrw8c10p54) A cylinder having a mass of 7.0 kg can rotate about its central axi

Question

(hrw8c10p54) A cylinder having a mass of 7.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 8.5 N, F2 = 3.5 N, F3 = 1.5 N, and F4 = 6.5 N. Also, R1 = 5.5 cm and R2 = 15.0 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 7.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 8.5 N, F2 = 3.5 N, F3 = 1.5 N, and F4 = 6.5 N. Also, R1 = 5.5 cm and R2 = 15.0 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 = 7.0 kg

   ??_net = I ?

moment of inertia I = 1/2 M R_2^2

                              

                                  = 1/2 * 7.0 kg * ( 0.15 m)^2

                                   = 0.07875 kg m^2

? ? = F_1 R_2 - F_2 R_2 -F_3 R_1 * F_4 * 0

         = 8.5 N * 0.15 m - 3.5 N * 0.15 m - 1.5N * 0.055 m

         = 0.6675 N m

angular acceleration ?   = ? ? / I

                                      = 0.6675 N m / 0.07875 kg m^2

                                      = 8.476 rad /s^2

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