(14%) Problem 4: A uniform disc of mass m-1 kg and radius R-0.55 m is suspended

Question

(14%) Problem 4: A uniform disc of mass m-1 kg and radius R-0.55 m is suspended horizontally by a wire. Refer to the figure. A force of F-45 N is applied to the edge of the disc tangentially. As a result, the disc turns and reaches equilibrium position at an angle of -1.9 rad from its initial orientation Otheexpertta.com 33% Part (a) Determine the value of the torsion constant of the wire, in units of Newton meters per radian Grade Summar Deductions Potential 0% 100% cosO Submissions Attempts remaining: 10 sinO) acos) sinh() cosh0 tanh0 cotanh0 % per attempt) detailed view atan) acotan) 0 Degrees Radians 0 Submit Hint Hints: 0% deduction per hint. Hints remaining: 1 Feedback: 0% deduction per feedback 33% Part (b) Determine the torque, in newton meters, that would be required to rotate the disc by one complete rotation 33% Part (c) If the disc is rotated as described above and then released, at what angular frequency, in radians per second, will it oscillate?

Explanation / Answer

(A) torque = k(theta)

(0.55 x 45) = k (1.9)

k = 13 N/m

(b) torque = k (theta)

for complete , theta = 2 pi

torque = 13(2pi) = 81.8 N m

(C) k (theta)^2 /2 = I w^2 /2

(13)(2pi)^2 / 2 = (1 x 0.55^2 / 2) w^2 / 2

w = 58.3 rad/s

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