Total Kinetic Energy: Man, Globe, Platform

[spirited]

Homework Statement

A man stands at the center of a turntable that can rotate without friction. He then takes a 1.5 kg globe of the Earth and swings it around his head at the end of a 0.7 m long chain. The world revolves around him every 3.4 s, and the man and the platform have a moment of inertia of 0.5 kgm^2. The angular velocity is 2.71 rad/s in the opposite direction to that of the globe. What is the total Kinetic Energy of the man, the globe, and the platform?

Homework Equations

K = 0.5Mv^2 of the globe + L^2/(2I) of the platform

The Attempt at a Solution

K total = 0.5Mv^2 + L^2/(2I)
K total = 0.5(1.5)(0.7x2pi/3.4)^2 + (0.5x2.71)^2/(2x0.5) = 3.091J

Plz. help... I do not think my answer is right... mainly the equation part...
-Thanks a lot...

 

[ak1948]

Looks right to me.

 

[thomate1]

Hello, thank you for your question. Your attempt at the solution is on the right track, but there are a few errors in your equations. Let's break it down step by step.

First, let's define our variables:
M = mass of the globe (1.5 kg)
v = velocity of the globe (calculated using its angular velocity and radius of rotation)
L = angular momentum of the platform (calculated using its moment of inertia and angular velocity)
I = moment of inertia of the platform (0.5 kgm^2)

Next, let's calculate the velocity of the globe. We know that the globe travels around the man every 3.4 seconds, so its angular velocity (ω) is 2π/3.4 rad/s. We also know that the globe has a radius of 0.7 m, so we can use the formula v = ωr to calculate its linear velocity:
v = (2π/3.4)(0.7) = 1.64 m/s

Now, let's calculate the angular momentum of the platform. We can use the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. Plugging in our values:
L = (0.5)(2.71) = 1.355 kgm^2/s

Finally, we can plug all of our values into the total kinetic energy equation:
K total = 0.5Mv^2 + L^2/(2I)
K total = 0.5(1.5)(1.64)^2 + (1.355)^2/(2x0.5) = 3.094 J

So, the total kinetic energy of the man, globe, and platform is approximately 3.094 Joules. I hope this helps clarify the equations for you. Remember to always double check your units and to use the correct formulas for each variable. Keep up the good work!