carnival ride rotation Billy is riding the Rotor ride at the carnival. This ride

Question

carnival ride rotation

Billy is riding the Rotor ride at the carnival. This ride is a cylindrical room that spins faster and faster until the floor drops out. The ride starts from rest, and after 15 seconds of constant angular acceleration the room has made a total of 6 revolutions. The radius of the room is 2 m. Find the angular acceleration of the room in rads/s^2. What is the final angular speed of the room? Find the magnitude of Billy's centripetal acceleration after the 15 s. Flow does this compare to the 10 m/s^2 acceleration due to gravity? What must be the coefficient of static friction between Billy and the wall if he is not to slide down the wall and fall out of the bottom?

Explanation / Answer

given data,

wo = 0

radius , R = 2 m

angular dispalacement in 6 seconds,

theta = 6 revoltuions

= 6*2*pi

= 37.7 rad

a) Apply, theta = wo*t + 0.5*alfa*t^2

theta = 0 + 0.5*alfa*t^2

==> alfa = 0.5*theta/t^2

= 2*37.7/15^2

= 0.335 rad/s^2

b) w = wo + alfa*t

= 0 + 0.335*15

= 15.3 rad/s

c) a_centripetal = r*w2^2

= 2*15.3^2

= 470.3

a_centripetal/g = 470.3/10

= 47.03

d)tangential acceleration, a_tan = r*alfa

= 2*0.335

= 0.67

we know, Normal force = m*a_rad

= m*470.3

so, static friction = N*mue_s

m*a_tan = m*a_rad*mue_s

==> mue_s = a_tan/a_rad

= 0.67/470

= 0.0014

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