If the radius of the grindstone is 0.50m..?

Question

If the radius of the grindstone is 0.50m (previous example, check link), calculate
a) Linear or tangential speed of a particle on the rim
b) Tangential acceleration of a particle on the rim
c) Centripetal acceleration of a particle on the rim at end of 2.0 sec
d) Are the results the same for a particle halfway in from the rim, that is, at r = 0.25 m?

This is a part 2 question, it was determined that w = 6 rad/sec and theta = 1.5t^2
link -> https://ca.answers.yahoo.com/question/index?qid=20191108031300AAh2aO6
(same image used)

Thank you,

NCS · Accepted Answer

Assuming you're interested in these properties at t = 2 s,

a) tangential v = ω*r = 6.0rad/s * 0.50m = 3.0 m/s

b) tangential a = α*r = 3.0rad/s² * 0.50m = 1.5 m/s²

c) centripetal a = ω²r = (6.0rad/s)² * 0.50m = 18 m/s²

d) No; all three values are proportional to the radius; at half the radius, all three values are halved

Hope this helps!

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If the radius of the grindstone is 0.50m..?

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