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 75.0 rev/min in 3.20 s?
b) when the disk is at its final speed, what is the tangential velocity of the bug? c) one second after the bug starts from rest, what is its tangential acceleration? d) one second after the bug starts from rest, what is its centripetal acceleration? e) one second after the bug starts from rest, what is its total acceleration?

0.38963 m/s²

1.246819325 m/s

0.38963 m/s²

0.95629 m/s²

1.03261 m/s² and 22.17°

Explanation:

d = Diameter of rim = 12.5 in =

r = Radius =

= Final angular velocity =

= Initial angular velocity = 0

= Angular acceleration

t = Time taken = 3.2 s

Equation of rotational motion

Tangential acceleration is given by

The tangential acceleration of the bug is 0.38963 m/s²

Tangential velocity is given by

The tangential velocity of the bug is 1.246819325 m/s

The tangential acceleration is constant which is 0.38963 m/s²

Centripetal acceleration is given by

The centripetal acceleration of the bug is 0.95629 m/s²

The resultant of the acceleration gives us total acceleration

Direction is given by

The magnitude and direction of the acceleration is 1.03261 m/s² and 22.17°

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