please answer it all (correct) A ceiling fan consists of a small cylindnca. disk

Question

please answer it all (correct)

A ceiling fan consists of a small cylindnca. disk with 5 thin rods coming from the center. The disk has mass m_d = 2.5 kg and radius R - 0.23 m. The rods each have mass m_r - 1.3 kg and length L - 0.89 m. What is the moment of inertia of each red about the axis of rotation? What s the moment of inertia of the disk about the ax s of rotation? What is the moment of inertia of the whole ceiling fan? When the fan is turned on, it takes t - 3.1 s and a total of 15 revolutions to accelerate up to its full speed. What is the magmtude of the angular acceleration? What is the final angular speed of the fan? What is the final rotational energy of the fan? 7) Now the fan is turned to a power setting where it ends with half of its rotational energy as before. The time it takes to slow to this new speed is also t - 3.1 s. What is the final angular speed of the fan? What is the magnitude of the angular acceleration while the fan slows down?

Explanation / Answer

here,

mass of disk, md = 2.5 kg
radius of disk, r = 0.23 m

mass of each rod, mr = 1.3 kg
length of roid,l = 0.88 m

Part a:
moment of inertia of rod about one end is given by,
Ir = (1/3)*Mr*L^2 = (1/3)*1.3* 0.88^2 = 0.336 Kg.m^2

Part b:
For disk, Moment of ienrtia,
Id = 0.5*md*r^2 = 0.5*2.5*(0.23)^2 = 0.066 Kg.m^2

Part c:
For whole Ceiling fan,
I = 5*Ir + Id = 5*0.336 + 0.066 = 1.746 Kg.m^2

Part D:
From Second Equation of rotational motion,
theta = 0.5*alpha*t^2
n*r*pi = 0.5*alpha*t^2 ( n is no of revolutions)

solving for angular speed,
alpha = 4*pi*N/t^2
alpha = 4*pi*15/(3.1)^2
alpha = 19.615 rad/s^2

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