Multiple-Concept Example 7 explores the approach taken in problems such as this

Question

Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.372 m and are rotating about a fixed axis with an angular velocity of +1.52 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 2.06 rad/s2. After 0.450 s have elapsed since the switch was reset, what are the following? (See figure below.)

Multiple-Concept Example 7 explores the approach taken in problems such as this one. The blades of a ceiling fan have a radius of 0.372 m and are rotating about a fixed axis with an angular velocity of +1.52 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 2.06 rad/s2. After 0.450 s have elapsed since the switch was reset, what are the following? (See figure below.)

Explanation / Answer

Angular velocity at 0.45s = 1.52+2.06*0.45 = 2.447rad/s

Tip velocity = radius*angular velocity = 0.91m/s

aT = r*angular acc. = 0.766m/s2

aC = V2/R = 2.22m/s2

/resultant = a 2.35m/s2

tan(phi) = aT/aC => phi = 19.03 degrees

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