(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 80.0 rev/min in 3.60 s?
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

(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*2.54*10^-2 = 0.3302 m
r = d/2 = 0.1651 m
wo = 0

w = 80 rev/min = 80*2*pi/60 = 8.373 rad/s


angular acceleration, alfa = (w-wo)/t = 8.373/3.6 = 2.33 rad/s^2


a_tan = r*alfa = 0.1651*2.33 = 0.385 m/s^2

b)

v = r*w = 0.1651*8.373 = 1.38 m/s

c)

same, a_tan = 0.395 m/s^2

d) w = wo+alfa*t = 0 + 2.33*1 = 2.33 rad/s

a_rad = r*w^2 = 0.1651*2.33^2 = 0.896 m/s^2

e) a = sqrt(a_tan^2+a_rad^2) = 0.975 m/s^2

theta = tan^-1(a_tan/a_rad) = 23.25 degrees

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