(a) What is the tangential acceleration of a bug on the rim of a 12.0 -in.-diame

Question

(a) What is the tangential acceleration of a bug on the rim of a 12.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 76.0 rev/min in 3.10 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

w = 76(2pie/1)(1/60) = 7.96 rad/s

r = 0.5(1/39.37) = 0.13 m

a) alpha = 7.96-0/3.1 = 2.57 rad/s^2

a_t = r alpha = 0.13*2.57 = 0.334 m/s^2

b) w = 7.96

v_t = rw = 0.13*7.96 = 1.04 m/s

c) a_c = v_t^2/r = 0.334^2/0.13 = 0.86 m/s^2

a= sqrt(a_c + a_t^2) = sqrt(0.86^2 + 0.334^2) = 0.79 m/s^2

theta = arc tan(0.334/0.86) = 21.22 degrees

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