Question

Problem # 2

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PHY 231 II1 Class Test Fall 2017 This is Class Test 3 (6 PM to 8 PM on 26th October 2017). Answer only 6. Each problem carries the same oints. Total point is 30 (5x6). You have to show the every step to solve the problem (2 points ex).1 point or correct formula. 1 point for correct figure and 1 point accuracy. 1) An airplane propeller is rotating at 2200 rpm (rev/min), (a) Compute the propeller's angu lar velocity in rad/s. (b) How many seconds does it take for the propeller to turn through 31.0 You are to design a rotating cylindrical axle to lift 700-N buckets of cement from the ground to a rooftop 68.0 m above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise. (a) What should the diameter of the axle be in order to raise the buckets at a steady 2.25 cm/s when it is turning at 7.6 rpm? (b) If instead the axle must give the buckets an upward acceleration of 0.345 m/s, what should the angular acceleration of the axle be? 2) 3) A centrifuge in a medical laboratory rotates at an angular speed of 2800 rpm (revolutions pe minute). When switched off, it rotates 47.5 times before coming to rest. Find the constant angula acceleration of the centrifuge. (Assume the initial direction of rotation is the positive directio Indicate the direction with the sign of your answer.) A thin liniform rod (length = 1.3 m. mass-41 kg) is pivoted about a horizontal frictionless 1)

Answer 1

(a) $v=R\omega \implies 2.25 cm/s= R \left ( \frac{7.6rev}{min} \right )*\left ( \frac{1min}{60sec} \right )*\left ( \frac{2\pi rad}{1rev} \right )$

therefore $R=\frac{2.25}{0.79}=2.84cm$

(b) $a_{tan}= R\alpha \implies \alpha =\frac{0.345}{0.0284}=12.14 rad/s^{2}$