# Calculate Total Energy: Solve Homework Statement

• Neon32
In summary, the problem involves finding the total energy of a bowling ball given its translational and rotational kinetic energy. The correct method is to use the given moment of inertia and square the angular velocity, resulting in a total energy of 49.152 Joules. The incorrect method used by another individual involved assuming the bowling ball is a uniform sphere and calculating the moment of inertia, as well as failing to square the angular velocity.
Neon32

## Homework Equations

Total energy = Translational kinetic energy + Rotational kinetic energy
Total energy= 1/2 m V2 + 1/2 I W2

## The Attempt at a Solution

W= v/r = 3.20/0.100 = 32 rad/sec
Total energy= 1/2 m V2+ 1/2 I W[2
Total energy = 1/2 (8)(3.20)2 + 1/2 (1.60x10-2) (32)2=49.152 Joule

I found a different answer in solution. Why did he find the moment of inerta? it was already given in the problem + why didn't he square the angular velocity? Please tell me why he did that and if my answer or his answer is correct.

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Your method and result are correct. His is not.

The problem did not say that the bowling ball is a sphere of uniform density: the fact that the problem supplied the moment of inertia is evidence of this. So his assumption that it is a uniform sphere was flawed and his calculation of the moment of inertia was not only unnecessary but incorrect.

That he failed to square the angular velocity is also an error.

Chestermiller
gneill said:
Your method and result are correct. His is not.

The problem did not say that the bowling ball is a sphere of uniform density: the fact that the problem supplied the moment of inertia is evidence of this. So his assumption that it is a uniform sphere was flawed and his calculation of the moment of inertia was not only unnecessary but incorrect.

That he failed to square the angular velocity is also an error.
Alright. thanks for your help :).

## What is total energy?

Total energy is the sum of all forms of energy in a system, including potential, kinetic, thermal, and chemical energy.

## How do I calculate total energy?

To calculate total energy, you need to know the individual forms of energy present in the system and use the appropriate formulas to calculate their values. Then, add up the values to get the total energy.

## What is the formula for calculating total energy?

The formula for calculating total energy depends on the specific forms of energy present in the system. For example, for a system with only kinetic and potential energy, the formula would be E = KE + PE. It is important to understand the specific forms of energy and their corresponding formulas in order to accurately calculate total energy.

## Why is it important to calculate total energy?

Calculating total energy allows us to understand the overall energy balance and dynamics of a system. It can also help us predict the behavior and changes of the system, and can be useful in various scientific and engineering applications.

## What are some common mistakes when calculating total energy?

Some common mistakes when calculating total energy include forgetting to account for all forms of energy present in the system, using incorrect formulas, and not considering the units of measurement. It is important to double check all calculations and make sure all forms of energy are properly included in the final value.

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