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 +1.43 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 0.455 s have elapsed since the switch was reset, what are the following? (See figure below.)

(a) the total acceleration (in m/s2) of a point on the tip of a blade 1.07 Incorrect: Your answer is incorrect. m/s2

(b) the angle between the total acceleration and the centripetal acceleration ac

the answer is not 1.07 and 45. they are not correct. please right clearly.

Explanation / Answer

According to the given problem,

After 0.455s, the angular velocity = i + t = 1.43 + 2.04*0.455 = 2.358rad/s

The centripetal acceleration = ²r = 2.358² * 0.372 = 2.0687m/s²

Since tangential velocity v = r, tangential acceleration, a = (d/dt)r = 2.04 * 0.372 = 0.7588m/s²

The tangential and centripetal accelerations are perpendicular vectors, so add using Pythagoras and find angle using tangent:

Total acceleration = (0.75888² + 2.0687²) = 2.2035m/s²

Angle = tan-1(0.75888/2.0687) = 20.1447º

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