**Doubling Units of Mass, Length, and Time and its Impact on Angular Momentum**

To understand the impact of doubling the units of mass, length, and time on the unit of angular momentum, we need to examine the definition and formula for angular momentum.

**Definition of Angular Momentum:**
Angular momentum is a property of rotating objects and is defined as the product of the moment of inertia and angular velocity. It quantifies the amount of rotational motion possessed by an object.

**Formula for Angular Momentum:**
Angular momentum (L) is calculated using the formula:
L = Iω
where:
- L is the angular momentum
- I is the moment of inertia
- ω is the angular velocity

**Impact of Doubling Units:**

When the units of mass, length, and time are doubled, it affects the calculation of angular momentum as follows:

1. **Mass (M):**
- Doubling the unit of mass (M) will result in a change in the moment of inertia (I).
- The moment of inertia depends on the distribution of mass in an object and is directly proportional to the square of the distance of mass elements from the axis of rotation.
- If we double the mass, the moment of inertia will increase by a factor of 4 (2^2).
- This means the angular momentum (L) will also increase by a factor of 4.

2. **Length (L):**
- Doubling the unit of length (L) does not directly affect the moment of inertia (I) unless there is a change in the distribution of mass.
- However, the angular velocity (ω) may be affected as it depends on the linear velocity (v) and the radius of rotation (r).
- If the length is doubled while keeping the same linear velocity, the radius of rotation will also double.
- As a result, the angular velocity will be halved (ω' = ω/2).
- Consequently, the angular momentum (L) will be halved (L' = Iω' = I(ω/2) = L/2).

3. **Time (T):**
- Doubling the unit of time (T) does not directly affect the moment of inertia (I) or the angular velocity (ω).
- Hence, the angular momentum (L) remains unaffected by the change in time units.

**Conclusion:**
Doubling the units of mass and length while keeping the time unit constant results in a four-fold increase in the angular momentum. However, doubling the time unit alone does not impact the angular momentum.

Dubbed