5%) Problem 4: A fan has four blades attached to a central shaft. The blades are

Question

5%) Problem 4: A fan has four blades attached to a central shaft. The blades are 1 19 cm long and blade have a niformly distributed mass of m 0.19 kg. The fan spins up from rest to an angular speed of r-11 l md s in 4-085 s. each 33% Part (a) Treat each fan blade as a uniform rod of length If rotating about its end. Enter an expression for the total change in th angular momentum Al of the fan during the spin up. Assume the angular momentum of the central shaft is insignificant. Grade Summ Potential 7 8 9 Attempts remai (5% per attemp detailed view Submit Hint Feedback: deduction per feedback. Hints-fora-)%, deduction, Hints remaining:- What is the expression for the moment of inertia of a rod rotating on its end? 33% Part (b) Give an expression for the average torque 33% Part (c) If the fan spins throu that the fan's motor exerts on the fan as it spins up gh 7.5 rotations during the spin up, calculate the work W in joules, that the fan's motor does on the f All comical 0.317 Expert TATLC

Explanation / Answer

Angular momentum of all 4 blades are same, and is equal to Iw . Change in angular momentum is final- initial angular momentum= Iw-0 = Iw

where I = moment of inertia of rod about the end = mL^2 / 3 and w= change in angular speed= final - initial angular speed= wf - 0=  wf

So, using above expressions, Iw= (mL^2 / 3) * ( wf ) {given values can be put in to find numerical value also, since expression is asked so only expression is found}

So, For fan with 4 blades, expression for total cahnge in angular momentum during the spin up is L = 4wfmL^2/ 3

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