A merry-go-round of diameter 2.7 m is rotating at a constant 4.15 rad/s and a bone...

A merry-go-round of diameter 2.7 m is rotating at a constant 4.15 rad/s and a bone is sitting at a spot on the MGR's rim. A puppy, initially at rest, notices the bone when 90 degrees behind the bone. If the puppy accelerates at 1.75 m/s² while running around the outer edge of the MGR find when the puppy can grab the bone. Bear in mind there are two possibilities: the puppy catches up to the bone OR the bone catches up with the puppy. Assume the puppy gets it at the first available opportunity.

ΔΘ=ω_i Δt + 1/2α(Δt)²
ΔΘ=1/2(ω_i+ω_f)Δt
ω_f=ω_i+α(Δt)
ω_f²=ω_i²+2α(ΔΘ)
2π r = 360 degrees
(πr)/2 = 90 degrees

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genius_generous answered 2 years ago

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