(a) What is the tangential acceleration of a bug on the rim of a 13.0 -in.-diame

Question

(a) What is the tangential acceleration of a bug on the rim of a 13.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 77.0 rev/min in 4.10 s?
m/s2

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

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

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

(e) One second after the bug starts from rest, what is its total acceleration?

Explanation / Answer

(e) One second after the bug starts from rest, what is its total acceleration?(a)final angular velocity = 80*2pi/60 = 8.378 rad/sec
rotational acceleration = 8.378/4.3 = 1.95 rad/s^2
radius = 13 in = 0.33 m
tangential acceleration = rotational acceleration*radius
= 0.644 m/s^2
(b) tangential velocity = 8.378*0.33 = 2.765 m/s

(c) tangential acceleration is constant over the entire time = 0.644 m/s^2

(d) angular velocity after 1 sec = 1.95 rad/sec
centripetal acceleration = ?^2 r = 1.95^2 * 0.33

= 1.255 m/s^2

(e) total acceleration = sqrt(0.644^2 + 0.33^2) = 0.723 m/s^2

angle from radially inward direction = tan^-1(0.644/0.33) = 62.87 degrees

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