a What is the tangential acceleration of a bug on the rim of

(a) What is the tangential acceleration of a bug on the rim of a 10.0 in. diameter disk if the disk moves from rest to an angular speed of 80 revolutions per minute in 5.0 s?
1 m/s²
(b) When the disk is at its final speed, what is the tangential velocity of the bug?
2 m/s
(c) One second after the bug starts from rest, what is its tangential acceleration?
3 m/s²
What is its centripetal acceleration?
4 m/s²
What is its total acceleration?
5 m/s²
6 ° (relative to the tangential acceleration)

Solution

a) initial angular speed wi = 0

final angular speed wf = 80 rpm = ( 80 x 2pi rad) / 60 s = 8.38 rad/s

using wf = wi + alpha*t

8.38 = 0 + alpha*5

alpha = 1.68 rad/s^2

tangential acc. = alpha*r = 1.68 x (10 x 0.0254) m/s^2 = 0.43 m/s^2

b)

v = wf *r = (8.38)*(10*0.0254) = 2.13 m/s

c) tangential acc. is constant = 0.43 m/s^2

after 1 sec , speed = 0.43*1 = 0.43 m/s

centripetal acc. ac = v^2 / r = (0.43^2) / (10 * 0.0254) = 0.73 m/s^2

total acc. = sqrt(ac^2 + at^2) = 0.84 m/s^2