A high school physics instructor catches one of his students chewing gum in clas

Question

A high school physics instructor catches one of his students chewing gum in class. He decides to discipline the student by asking that he stick the gum to a fan and calculate how fast the fan is moving when the gum gets thrown off The label says that the diameter of the fan is d = 32 cm, and at full speed it turns at a rate of f = 25 rev/s. and that the fan is guaranteed to accelerate uniformly. The fan takes t = 11s to go from rest to full speed. Randomized Variables d = 32 f = 25 rev/s t = 11 s Calculate the maximum the angular velocity of the fan omega_max. in radians per second. Numeric A numeric value is expected and not an expression. Omega_max = Surprisingly, the gum seems to remain stuck to the fan at this speed. Calculate the angular acceleration of the gum a, in radians per square second, as the fan is speeding up. Numeric A numeric value is expected and not an expression. Alpha = Calculate the tangential component of the acceleration of the gum a_tan, in meters per square second, as the fan is speeding up. Numeric A numeric value is expected and not an expression. What is the magnitude of the centripetal acceleration of the gum a_rad, in petal meters per square second, when the fan reaches full speed? Numeric A numeric value is expected and not an expression. A_rad = What is the direction of the centripetal acceleration of the gum, as the fan is turning at top speed? 1) Radially outward. 2) Radially inward. 3) There is no radial component of the acceleration. 4) In the direction of rotation. 5) Opposite the direction of rotation. Calculate the tangential component of the acceleration of the gum a _tan f, in meters per square second, when the fan is at full speed. Numeric A numeric value is expected and not an expression. a_tan, f = Soon after reaching this speed, the gum becomes un-stuck from the fan blade. Determine the linear speed off the gum v, in meters per second, immediately after it leaves the fan. Numeric A numeric value is expected and not an expression.

Explanation / Answer

Given:-

d=0.32 m

wf= 25 rev/s= 25*2 pie rad/s= 157 rad/s

t= 11s

wi=0 rad/s

a] Here maximum w max= wf= 25 rev/s= 25*2 pie rad/s= 157 rad/s

b] wf= wi+ t

= wf-wi/t= [157 rad/s-= 0 rad/s] / 11s= 14.3 rad/s2

= 14.3 rad/s2

c] Tangential component of acceleration , atan= d* = 0.32 m* 14.3 rad/s2= 4.58 m/s2

d] Radial component= tangential component of acceleration , atan= d* = 0.32 m* 14.3 rad/s2= 4.58 m/s2

e] Radially outward

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