What is the magnitude of the tangential acceleration of a bug on the rim of an 1

Question

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 3.90 s? When the disk is at its final speed, what is the magnitude of the tangential velocity of the bug? One second after the bug starts from rest, what is the magnitude of its tangential acceleration? One second after the bug starts from rest, what is its total acceleration? (Take the positive direction to be in the direction of motion.)

Explanation / Answer

here,

diameter , d = 11 in
radius , r = 11/2 in = 5.5 in = 0.134 m
angular speed , w = 79 rev/min = 8.27 rad/s
time taken , t = 3.9 s

(a)
let the angular accelration be a
using first equation of motion
w = 0 + a*t
8.27 = 0 + a*3.9
a = 2.12 rad/s^2

at = a*r
at = 2.12*0.134
at = 0.294 m/s^2

the magnitude of the tangential accelration is 0.294 m/s^2

(b)
magnitude of the tangential velocity , v = r*w
v = 0.134 * 8.27
v = 1.108 m/s

magnitude of the tangential velocity is 1.108 m/s

(c)
tangential accelration remains contant as centripital accelration is constant, so

the tangential accelration(at) will be 0.294 m/s^2

(d)
when t = 1 s
w = a*t
w = 0.294*1
w = 0.294 rad/s

the magnitude of the centripital accelration , ac = w^2*r
ac = 0.294^2 * 0.134
ac = 0.0116 m/s^2

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