the flywheel is so constructed that the entire mass of it is concentrated at its rim, because

Options

A. it increases the moment of inertia of the fly-wheel
B. it decreases the moment of inertia of the fly-wheel
C. it increases the speed of the fly-wheel
D. it increases the power of the fly-wheel

Answer

To solve the question regarding why a flywheel is constructed such that its entire mass is concentrated at its rim, we can follow these steps:

### Step 1: Understanding the Flywheel
A flywheel is a mechanical device that stores rotational energy. It typically has a large mass and is designed to maintain a consistent rotational speed.

**Hint:** Consider the purpose of a flywheel in mechanical systems.

### Step 2: Analyzing the Mass Distribution
In this case, the question states that the entire mass of the flywheel is concentrated at its rim. This means that all the mass is located at the maximum distance from the axis of rotation.

**Hint:** Think about how mass distribution affects rotational motion.

### Step 3: Moment of Inertia
The moment of inertia (I) of an object is a measure of its resistance to changes in its rotational motion. For a point mass, the moment of inertia is given by the formula:
\[ I = m \cdot r^2 \]
where \( m \) is the mass and \( r \) is the distance from the axis of rotation.

**Hint:** Recall the formula for moment of inertia and how it relates to mass and radius.

### Step 4: Maximum Radius
Since the mass is concentrated at the rim, the radius \( r \) is at its maximum. This leads to a higher moment of inertia because:
- If \( r \) is maximized, then \( I \) will also be maximized since \( I \) is directly proportional to \( r^2 \).

**Hint:** Consider how increasing the radius affects the moment of inertia.

### Step 5: Implications of High Moment of Inertia
A higher moment of inertia means that the flywheel will have greater stability and can store more rotational energy. This is beneficial in applications where maintaining a consistent speed is crucial, such as in engines or machinery.

**Hint:** Reflect on the advantages of having a high moment of inertia in mechanical systems.

### Conclusion
Thus, the reason the flywheel is constructed with its mass concentrated at the rim is to **increase the moment of inertia**, allowing it to store more energy and maintain a steady rotational speed.

**Final Answer:** The flywheel is constructed such that the entire mass is concentrated at its rim to increase the moment of inertia of the flywheel.