(a) What is the tangential acceleration of a bug on the rim of a 8.0 in. diamete

Question

(a) What is the tangential acceleration of a bug on the rim of a 8.0 in. diameter disk if the disk moves from rest to an angular speed of 76 revolutions per minute in 3.0

_____________m/s2
(b) When the disk is at its final speed, what is the tangential velocity of the bug?
___________ m/s
(c) One second after the bug starts from rest, what is its tangential acceleration?
____________ m/s2
What is its centripetal acceleration?
_____________ m/s2
What is its total acceleration?

_____________m/s2
______

Explanation / Answer

a) w1 = 0,

w2 = 76 rpm = 76*2*pi/60 = 7.955 rad/s

alfa = (w2-w1)/t = (7.955-0)/3*60 = 0.442 rad/s^2

d = 8 inch = 8*2.54 = 20.32 cm = 0.2032 m

r = d/2 = 0.1016 m

a_tan = r*alfa = 0.1016*0.442 = 0.045 m/s^2

b)

v = r*w2 = 0.1016*7.955 = 0.808 m/s

c) at t = 1

w = w1 + alfa*t = 0 + 0.442*1 = 0.442 rad/s

a_rad = r*w^2 = 0.1016*0.442^2 = 0.198 m/s^2

a = sqrt(a_rad^2+a_tan^2) = 0.492 m/s^2

theta = tan^-1(a_rad/a_tan) = 77.2 degrees

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