How Does a Spinning Platform Affect the Period of a Pendulum?

[ataglance05]

Homework Statement

A pendulum 2 meters long with a mass of 1kg is mounted on a circular platform on the Earth's surface that's spinning at constant angular velocity of .12 rads/sec. The pendulum is mounted on a pole that's perpendicular to the platform at a distance of 5 meters from the center of rotation.

If it's displaced for its equilibrium position, what will be the period of the pendulum?

P.S. My physics teacher said that the diagrams below explains what's happening:

FROM A BIRD'S EYE VIEW-
http://answerboard.cramster.com/answer-board/image/43e827330329f2500585d3862fc2f7af.jpg

FROM A NORMAL VIEW:
http://answerboard.cramster.com/answer-board/image/2bf7be21984fbe2a0b76f2f86b744710.jpg

Now, he mentioned how we must get the force from the equation F=mv2/r and then get the acceleration from a=F/m, but first I need to get r and I have no clue how to do that since theta isn't given. Then I have to replace the acceleration I get for g in the period equation.
Please help!

Homework Equations

a=F/m
a=v2/r
F=mv2/r

The Attempt at a Solution

No clue!?

 

[Mentz114]

Do you know how to work out the period of a pendulum that's not on a turntable ?

One of the numbers in the equation is the 'return force' on the bob. You'll need to replace that with a different force for the rotating pendulum.

 

[m2003]

As a scientist, it is important to always start with what is given in the problem. In this case, we are given the length and mass of the pendulum, as well as the angular velocity and distance from the center of rotation. We can use these values to calculate the force and acceleration of the pendulum.

First, we can calculate the force using the equation F=mv^2/r, where m is the mass, v is the velocity (which we can calculate using the angular velocity and distance from the center), and r is the radius (which is given as 5 meters).

Next, we can use the equation a=F/m to find the acceleration of the pendulum. This will be the acceleration due to gravity, as the pendulum is being pulled towards the center of rotation.

Finally, we can use the equation for the period of a pendulum, T=2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. We can substitute the acceleration we calculated in the previous step for g, and solve for the period.

As for the diagrams provided, they show the pendulum at different points in its motion. The bird's eye view shows the pendulum at its maximum displacement from equilibrium, while the normal view shows the pendulum at its equilibrium position. These diagrams can be helpful in visualizing the problem, but they are not necessary for solving it.

In summary, to find the period of the pendulum in this scenario, we need to calculate the force, acceleration, and use the equation for the period of a pendulum. It is important to carefully consider the given information and use the appropriate equations to solve the problem.