m/s 2 Your response differs from the correct answer by more than 100%. What is t

Question

m/s2
Your response differs from the correct answer by more than 100%. 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 4.30 s? When the disk is at its final speed, what is the tangential velocity of the bug? One second after the bug starts from rest, what is its tangential acceleration? One second after the bug starts from rest, what is its centripetal acceleration? Your response differs from the correct answer by more than 10%. Double check your calculations. m/s2 One second after the bug starts from rest, what is its total acceleration?

Explanation / Answer

12 in = 0.3048 meters
76 revolutions per minute = (76/60)*2pi= 7.95 rad/sec

(a) angular acceleration = (7.95 rad/sec)/4.3 s = 1.848 rad/s^2
tangential acceleration = 1.848*0.3048 = 0.563 m/s^2

(b) tangential acceleration = 0 m/s^2, there is no more angular acceleration.

(c) tangential acceleration = 0.563 m/s^2; same as (a)

tangential speed = tangential acceleration * time = 0.563 m/s^2 * 1 sec = 0.563 m/s
a = (v^2)/r = (0.563^2)/0.3048 = 1.03 m/s^2

total acceleration = sqrt(0.563^2 + 1.03^2) = 1.17 m/s^2
direction relative to the tangential acceleration = tan^-1(1.03/0.563) = 61.21 degrees towards the center

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