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 0.363 m and are rotating about a fixed axis with an angular velocity of +1.56 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 2.04 rad/s2. After 0.495 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 0.363 m and are rotating about a fixed axis with an angular velocity of +1.56 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of 2.04 rad/s2. After 0.495 s have elapsed since the switch was reset, what are the following? the total acceleration (in m/s2) of a point on the tip of a blade the angle phi between the total acceleration and the centripetal acceleration ac

Explanation / Answer

w1 = 1.56 rad/s

w2 = w1+alfa*t = 1.56 + 2.04*0.495 = 2.5698 rad/s

a)

a_tan = r*alfa = 0.363*2.04 = 0.74052 m/s^2

a_rad = r*w2^2 = 0.363*2.5698^2 = 2.397 m/s^2

a_total = sqrt(a_rad^2 + a_tan^2) = 2.509 m/s^2

b)

theta = tan^-1(a_rad/a_tan) = 72.84 degrees

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