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

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 79.0rev/min in 4.80s?

b) When the disk is at it's final speed, what is the magnitude of the tangential velocity of the bug?

c) One second after the bug starts from rest, what is the magnitude of its tangential acceleration?

d) One second after the bug starts from rest, what is the magnitude of its centripetal acceleration?

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/s^2

Direction: _________degrees from the radially inward direction  

Explanation / Answer

given,

diameter = 12.5 in or 0.3175 m

final speed = 79 rev/min or 8.273 rad/sec

initial speed = 0 rad.sec

time = 4.8 sec

tangential velocity = angular speed * radius

tangential velocity = 8.273 * 0.3175

tangential velocity = 2.626 m/s

angular acceleration = 8.273 / 4.8

angular acceleration = 1.723 rad/sec^2

tangential acceleration = 1.723 * 0.3175

tangential acceleration = 0.547 m/s^2

centripetal acceleration = v^2 / r

centripetal acceleration = 2.626^2 / 0.3175

centripetal acceleration = 21.719 m/s^2

total acceleration = sqrt(21.719^2 + 0.547^2)

total acceleration = 21.726 m/s^2

angle = tan^-1(0.547 / 21.719)

angle = 1.443 degree

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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