Question

(a) What is the magnitude of the tangential acceleration of a bug on the rim of a 10.5-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 76.0 rev/min in 4.00 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)

from the rotational kinematic equation

wf = wi + alpha t

76 ( 2pi/60) = 0+ alpha ( 4)

alpha = 1.98 rad/s^2

at = r alpha = 5.25 in ( 0.0254 m) ( 1.98 = 0.265 m/s^2

(b)

v = rw =  5.25 in ( 0.0254 m)*76 ( 2pi/60) = 1.06 m/s

(c)

wf= alphat t = 1.98 ( 1) = 1.98 rad/s^2

1.98 = 0 + alpha * 1s

alpha = 1.98 rad/s^2

at = r alpha = 5.25 in ( 0.0254 m) ( 1.98 = 0.265 m/s^2

(d)

ac = r w^2 =  5.25 in ( 0.0254 m) ( 1.98)^2 = 0.522 m/s^2

(e)

a = sqrt ac^2 + at^2 = sqrt ( 0.265)^2 + ( 0.522)^2 = 0.586 m/s^2

theta = tan^-1 ( 0.522/0.586) = 41.58 degree