An amusement park ride consists of a large vertical cylinder that spins about it

Question

An amusement park ride consists of a large
vertical cylinder that spins about its axis fast
enough that a person inside is stuck to the
wall and does not slide down when the floor
drops away.
The acceleration of gravity is 9.8 m/s2 .
Given g = 9.8 m/s2, the coefficient µ =
0.559 of static friction between a person and
the wall, and the radius of the cylinder R =
5.9 m. For simplicity, neglect the person’s
depth and assume he or she is just a physical
point on the wall. The person’s speed is
v =
2R
T
where T is the rotation period of the cylinder
(the time to complete a full circle).
Find the maximum rotation period T of the
cylinder which would prevent a 54 kg person
from falling down.
Answer in units of s

Explanation / Answer

we have, a. mg = f mg = uN mg = u mv^2/R v^2 = gR/u speed = v = 10.17 m/s b. w = v/R = 1.723 rad/s w = 2pi/T = 1.723 Time period = T = 1 second

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