Starting from rest, a Ferris wheel of diameter 30.0 m undergoes an angular acceleration of 0.0400 rad/s2. A certain rider is at the lowest point of the wheel just as it starts to move. A) Find the velocity of the rider just as he completes a quarter of a turn.
B) Find the radial and tangential components of his acceleration at the same point.
C) How much farther must the wheel turn before the rider attains a speed of 6.00 m/s (the maximum that occurs during the ride)?
a. 5.32 m/s, up.
b. 0.600 m/s2, up.
1.88 m/s2 toward center.
d. 24.6°.

Solution :

Given :

Diameter, D = 30 m

∴ Radius, R = 15 m

Angular acceleration, α = 0.044

a). Velocity of the rider just as he completes a quarter of a turn is :

V = R ω

∴

∴

    = 5.32 m/s up

b). Tangential acceleration

        = 0.04 x 15

         up

Radial acceleration,

    towards center.

c). Final angular velocity

   given :

  = 0.43 rad

or

b) returns freshwater to the earth.

c) returns freshwater to the earth.c) occurs after condensation.

d) returns freshwater to the earth.c) occurs after condensation.d) roughly equal to the amount of evaporation.

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