Question

A 6 kg penguin gets onto a Ferris Wheel, with a radius of 5m, and stands on a bathroom scale. The wheel starts rotating with a constant acceleration of .001 rad/s2 for two minutes and then runs at a constant angular velocity. After the wheel is rotating at a constant rate, what is the penguin’s a) angular momentum about the center of the Ferris Wheel, b) tangential velocity c) maximum & minimum readings on the bathroom scale (and where do they occur?)

Answer 1

Part a)

`L = 18 kg m^2/s`

Part b)

`v = 0.6 m/s`

Part c)

`R_(max) = 6.04 kg`

`R_(min) = 5.96 kg`

Step-by-step explanation:

As we know that Ferris wheel start from rest with angular acceleration

`\alpha = 0.001 rad/s^2`

time taken = 2 min

so here we have its angular speed after t = 2min given as

`\omega = \alpha t`

`\omega = (0.001)(2* 60)`

`\omega = 0.12 rad/s`

Part a)

Angular momentum of the Penguine about the center of the wheel is given as

`L = I\omega`

`L = (6* 5^2)(0.12)`

`L = 18 kg m^2/s`

Part b)

tangential speed is given as

`v = r\omega`

`v = (5)(0.12)`

`v = 0.6 m/s`

Part c)

Maximum reading of the scale at the lowest point is given as

`R_(max) = (m\omega^2 r + mg)/(g)`

`R_(max) = (6(0.12^2)(5) + 6(9.81))/(9.81)`

`R_(max) = 6.04 kg`

Minimum reading of the scale at the top point is given as

`R_(min) = (mg - m\omega^2 r)/(g)`

`R_(min) = (6(9.81) - 6(0.12^2)(5))/(9.81)`

`R_(min) = 5.96 kg`