(a) What is the tangential acceleration of a bug on the rim of a 13.0 -in.-diame

Question

(a) What is the tangential acceleration of a bug on the rim of a 13.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 75.0 rev/min in 3.30 s?
m/s^2

(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

(d) One second after the bug starts from rest, what is its centripetal acceleration?
m/s2

(e) One second after the bug starts from rest, what is its total acceleration?

Explanation / Answer

a) d = 13 inch = 13*2.54*10^-2 = 0.3302 m

r = d/2 = 0.1651 m

w1 = 0, w2 = 75rpm = 7.85 rad/s

alfa = (w2-w1)/t = 2.38 rad/s^2

a_tan = r*alfa = 0.1651*2.38 = 0.393 m/s^2

b) v = r*w2 = 0.1651*7.85 = 1.296 m/s

c)

w = wo + alfa*t

w = 0 + 2.38*1 = 2.38 rad/s

v = r*w = 0.393 m/s

d) a_rad = v^2/r = 0.835 m/s^2

e) a_total = sqrt(a_tan^2 - a_rad^2) = 1.0144 m/s^2

theta = tan^-1(a_tan/a_rad) = 25.2 degrees

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