A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from

Question

A ceiling fan consists of a small cylindrical 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 = 0.88 m. 1) What is the moment of inertia of each red about the axis of rotation? 2) What is the moment of inertia of the disk about the axis of rotation? 3) What is the moment of inertia of the whole ceiling fan? 4) 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 magnitude of the angular acceleration? 5) What is the final angular speed of the fan? 6) What is the final rotational energy of the fan? 7) Now the fan is turned to a lower 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? 8) What is the magnitude of the angular acceleration white the fan slows down?

Explanation / Answer

1) 1/3*Mr*L^2= 0.343 kg m^2..........

2) (1/2) Md*R^2=0.066 kg m^2.........................

3) 5* 1/3*Mr*L^2+ (1/2) Md*R^2 = 1.781125kg m^2.........................

4)alpha =2*theta/t^2=2*15*2*3.14/3.2^2=18.3984 rad/s^2..........................

5) Wf = alpha *t = 58.875 rad/s......

6) KE = 0.5*I*Wf^2= 0.5*1.781125* 58.875^2= 3.086926181e+3 J..=3086.9J.............

7) KEf = KE/2 = 1.543463091e+3 J.........KE f = 0.5*I*W^2====>W = 41.63rad/s........

8) alpha = 41.63-58.87/3.2= −5.3875 rad/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.