Question

a) What is the magnitude of the tangential acceleration of a bug on the rim of a 12.5-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 76.0 rev/min in 4.70 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

here,

initial angular speed , w0 = 0 rad/s

final angular speed , w = 76 rev/min

w = 7.95 rad/s

time taken ,t = 4.7 s

let the angular acceleration be alpha

using first equation of motion

w = w0 + alpha * t

7.95 = 0 + alpha * 4.7

alpha = 1.69 rad/s^2

diameter , d = 12.5 in = 0.31 m

radius , r = d/2 = 0.155 m

the tangential acceleratio , at = r * alpha

at = 0.155 * 1.69 m/s^2 = 0.26 m/s^2

b)

the magnitude of the tangential velocity of the bug is 0.26 m/s^2

c)

the magnitude of its tangential acceleration is 0.26 m/s^2

d)

after t1 = 1 s

the angular speed , w1 = w0 + alpha * t

w1 = 0 + 1.69 rad/s = 1.69 rad/s

the magnitude of centripetal acceleration , ac = w1^2 * r

ac = 1.69^2 * 0.155 m/s^2 = 0.44 m/s^2

e)

the magnitude of total acceleration , a = sqrt(at^2 + ar^2)

a = sqrt(0.26^2 + 0.44^2 ) = 0.51 m/s^2

the direction , theta = arctan(at/ar)

theta = arctan(0.26 /0.44)

theta = 30.6 degree