The momentum of a car moving at a constant speed in a circular track

Analysis of the Question

The question asks about the nature of the momentum of a car moving at a constant speed along a circular track. To answer this, we must look at the definition of momentum and how it behaves in circular motion.

Concept Explanation

1. Definition of Momentum ($p$): Momentum is a vector quantity defined as the product of mass ($m$) and velocity ($v$): $$p = m \times v$$
2. Vector Nature: Because velocity is a vector (it has both magnitude and direction), momentum is also a vector. This means that for momentum to remain constant, both the speed and the direction of the object must remain constant.
3. Circular Motion: When a car moves in a circular track, even if its speed is constant, its direction is constantly changing at every point along the circle.
4. Directional Change: Since the direction changes, the velocity vector changes. Consequently, the momentum vector changes continuously as the car moves around the track. Because the direction is constantly shifting, the momentum can point in any direction (positive, negative, or any angle in between) relative to a fixed coordinate system.

Step-by-Step Solution

• Step 1: Recognize that momentum is a vector quantity ($\vec{p} = m\vec{v}$).
• Step 2: In a circular path, the velocity vector is always tangent to the circle. As the car moves, the tangent points in different directions.
• Step 3: Because the direction of the velocity vector changes, the direction of the momentum vector changes.
• Step 4: If we define a coordinate system (e.g., an x-axis), the momentum component along that axis will change from positive to negative as the car completes its orbit. Therefore, the momentum can be described as having both positive and negative values depending on the car's position and the chosen reference frame.

Evaluation of Options

• Option A: Correct. Since the direction of the momentum vector changes continuously, its components along any fixed axis will fluctuate between positive and negative values.
• Option B: Incorrect. Momentum is $p = mv$. Since the car has mass and is moving (speed > 0), the magnitude of momentum ($p = mv$) can never be zero.
• Option C: Incorrect. Inertia is related to mass, and as long as the car has mass and speed, momentum exists.
• Option D: Incorrect. "Centrifugal" is a force, not a description of momentum.

Exam Tip

Always remember the difference between speed (a scalar) and velocity (a vector). In circular motion, speed is constant, but velocity is never constant because the direction is always changing. Since momentum depends on velocity, it is also never constant in circular motion!