What is the tangential acceleration of a bug on the rim of a 6.0 in. diameter di

Question

What is the tangential acceleration of a bug on the rim of a 6.0 in. diameter disk if the disk moves from rest to an angular speed of 76 rev/min in 5.0 s? (?) m/s (squared) (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/s (squared) (?) m/s (squared) What is its centripetal acceleration? (?) m/s (squared) What is its total acceleration? (?) m/s (squared) and (?) degrees (relative to the tangential acceleration)

Explanation / Answer

6 in = 0.1524 meters
76 revolutions per minute = 76/60*2pi= 7.958 rad/sec

(a) angular acceleration = (7.958 rad/sec)/5.0 s = 1.59174 rad/s^2
tangential acceleration = 1.59174*0.1524 = 0.242 m/s^2

(b) tangential acceleration = 0 m/s^2, there is no more angular acceleration.

(c) tangential acceleration = 0.242 m/s^2; same as (a)

tangential speed = tangential acceleration * time = 0.242 m/s^2 * 1 sec = 0.242 m/s
a = (v^2)/r = (0.242^2)/0.1524 = 0.384 m/s^2

total acceleration = sqrt(0.242^2 + 0.384^2) = 0.4537 m/s^2
direction relative to the tangential acceleration = tan^-1(0.384/0.242) = 57.7 degrees towards the center.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.