# Answer to Question #120972 in Mechanics | Relativity for Mamart Sanchez

Question #120972
A fan blade is initially rotating an angular speed of 4.6 rpm. It slows down and eventually comes to rest in a time of 32 seconds after turning through a total of 8.8 revolution. Find a.) The angular speed in rad/s. b.) The average angular velocity ang c.) The average angular acceleration.
1
2020-06-09T13:20:14-0400

Initial angular velocity is "\\omega_o=4.6\\times \\frac{2\\pi}{60}=0.48\\:rad\/s"

Final time "t=t_f=32s" and angle traversed is "\\theta=8.8\\times2\\pi=55.29 \\:rad"

(a).As we have not provided at which time we need to find the angular speed, thus

we assume time t is arbitrary, hence

As angular acceleration is decreasing.

(b). Since, average angular velocity is given by

"\\omega_{av}=\\frac{\\Delta \\theta}{\\Delta t}"

Thus, on plugin the value we get,

(c). Since,

"\\alpha_{av}=\\frac{\\Delta \\omega}{\\Delta t}=\\frac{\\omega_f-\\omega_o}{t_f-t_o}"

Hence, on plugin the value we get

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