(hrw8c10p54) A cylinder having a mass of 10.0 kg can rotate about its central ax

Question

(hrw8c10p54) A cylinder having a mass of 10.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 10.0 N, F2 = 5.0 N, F3 = 1.5 N, and F4 = 6.5 N. Also, R1 = 5.5 cm and R2 = 13.0 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 10.0 kg can rotate about its central axis through point O. Forces are applied as in the figure: F1 = 10.0 N, F2 = 5.0 N, F3 = 1.5 N, and F4 = 6.5 N. Also, R1 = 5.5 cm and R2 = 13.0 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

cosidering clockwise Moments as -ve and anti clock wise moemnts as +ve

we have

(F1-F2)R2 - F3 * R1 + F4 *0   = Toprque

so T   = (10-5)* 0.13 - (1.5 * 0.055) + (6.5) *0

T = 4.86 Nm

now use TOrque T = I Alpha

where I = moment of Inertia   = mR^2/2

so

Ang Acccleration A    = T/I

A = 2T/mR^2

A = 2* 4.86/(10 * 0.13*0.13)

A = 57.51 rad/s^2

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