Question

(a) What is the magnitude of the tangential acceleration of a bug on the rim of an 11.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 79.0 rev/min in 4.50 s? m/s2

(b) When the disk is at its final speed, what is the magnitude of the tangential velocity of the bug? m/s

(c) One second after the bug starts from rest, what is the magnitude of its tangential acceleration? m/s2

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

(e) One second after the bug starts from rest, what is its total acceleration? (Take the positive direction to be in the direction of motion.) magnitude m/s2

direction ° from the radially inward direction

Answer 1

(a)

d = 2.54*11/100 = 0.27940 m

ω = (2PI/60)*n = 0.1047*79 = 8.27 rad/sec

V = ω*r = 8.27 *0.27940/2 = 1.156 m/sec

a = ΔV/Δt = 1.156/4.50 = 0.257 m/sec^2

(b)

V = ω*r = 8.27*0.27940/2 = 1.156 m/sec

(c)

tangential accelerationis constant and equal to 0.257 m/sec^2

(d)

V = a*t = 0.257 m/sec^2*1 sec = 0.257 m/sec

ac = V^2/r = 0.257^2*2/0.27940 = 0.473 m/sec^2

(e)

a = √at^2+ac^2 = √0.257^2+0.473^2 = 0.538 m/sec^2

° from the radially inward direction = arctan (257/473) = 28.52