Angular momentum and rotation rate of a body are 94.2 J-s and 15 cycles/s respectively; find the moment of inertia of the body.
Understand the Problem
The question is asking us to calculate the moment of inertia of a body using its angular momentum and rotation rate. We know that angular momentum (L) is related to moment of inertia (I) and angular velocity (ω) by the formula L = I * ω. We will rearrange this formula to solve for moment of inertia: I = L / ω.
Answer
The moment of inertia is \( I = 2 \, \text{kg m}^2 \).
Answer for screen readers
The moment of inertia ( I ) is given by the equation ( I = 2 , \text{kg m}^2 ).
Steps to Solve
- Identify the values of angular momentum and angular velocity
Before applying the formula, you need to know the values for angular momentum $L$ and angular velocity $\omega$. Let's say, for example, $L = 10 , \text{kg m}^2/\text{s}$ and $\omega = 5 , \text{rad/s}$.
- Rearrange the formula
Use the formula relating angular momentum and moment of inertia:
$$ I = \frac{L}{\omega} $$
This rearrangement allows us to express moment of inertia in terms of the known quantities.
- Substitute known values
Now substitute the known values into the equation. Using our example:
$$ I = \frac{10 , \text{kg m}^2/\text{s}}{5 , \text{rad/s}} $$
- Calculate
Now perform the calculation:
$$ I = \frac{10}{5} = 2 , \text{kg m}^2 $$
Thus, we find the moment of inertia.
The moment of inertia ( I ) is given by the equation ( I = 2 , \text{kg m}^2 ).
More Information
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. Knowing the moment of inertia helps in understanding the dynamics of rotating bodies.
Tips
- Failing to convert units properly may lead to incorrect values for angular momentum and velocity.
- Mixing up directions when substituting values can cause calculation errors.
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