A purse at radius 1.60 m and a wallet at radius 3.20 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (1.70 m/s2)i + (4.20 m/s2)j. At that instant and in unit-vector notation, what is the acceleration of the wallet?
I could really use some help. I've tired different ways to solve the problem but I can't get the right answer. Please Explain.
I could really use some help. I've tired different ways to solve the problem but I can't get the right answer. Please Explain.
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Isn't the answer
(3.40 m/s2)i + (8.40 m/s2)j ?
Since the motion is uniform circular motion, the acceleration is strictly centripetal, which would be
a = rω^2
ω is the rotation rate (r.p.m but usually measured in radians per second)
ω would be the same for purse and wallet because they are both rotating on the same platform so ω^2 would also be the same. What is different is r. R is twice as much for the wallet (3.20m / 1.60m = 2). So acceleration would be doubled to
2 X [(1.70 m/s2)i + (4.20 m/s2)j]
= (3.40 m/s2)i + (8.40 m/s2)j
(3.40 m/s2)i + (8.40 m/s2)j ?
Since the motion is uniform circular motion, the acceleration is strictly centripetal, which would be
a = rω^2
ω is the rotation rate (r.p.m but usually measured in radians per second)
ω would be the same for purse and wallet because they are both rotating on the same platform so ω^2 would also be the same. What is different is r. R is twice as much for the wallet (3.20m / 1.60m = 2). So acceleration would be doubled to
2 X [(1.70 m/s2)i + (4.20 m/s2)j]
= (3.40 m/s2)i + (8.40 m/s2)j