(a) What is the tangential acceleration of a bug on the rim of a 9.0 in. diameter disk if the disk moves from?

Question

(a) What is the tangential acceleration of a bug on the rim of a 9.0 in. diameter disk if the disk moves from rest to an angular speed of 78 revolutions per minute in 5.0 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
What is its centripetal acceleration? 
  

 m/s2
What is its total acceleration?
  

 m/s2 
  

 ° (relative to the tangential acceleration)

Woodsman · Accepted Answer

α = Δω / Δt = (78rev/min * 2πrad/rev * 1min/60s) / 5s = 8.17rad/s / 5s = 1.63 rad/s²

a) tangential a = α r = 1.63rad/s * (9in * 0.0254m/in) = 0.37 m/s²

b) v = ωr = 8.17rad/s * (9in * 0.0254m/in) = 1.87 m/s

c) tangential acceleration still 0.37 m/s²
centripetal acceleration a = ω²r = (α t)² r = (1.63rad/s² * 1s)² * (9in * 0.0254m/in)
a = 0.61 m/s²

I believe that the total acceleration is the sqrt of the sum of the squares, but I'm not certain.

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(a) What is the tangential acceleration of a bug on the rim of a 9.0 in. diameter disk if the disk moves from?

1 Answer