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General SciencePhysics: Motion and Force

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A particle moves in a circle of radius 2 m with a constant speed of 4 m/s. What is its centripetal acceleration?

2 m/s²

4 m/s²

8 m/s²

16 m/s²

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics: Motion and Force

Option C

8 m/s²

Quick Summary:

Centripetal acceleration is the rate of change of tangential velocity in a circular path. For a particle moving with a constant speed $v$ in a circle of radius $r$ , it is calculated using the formula $a_c = \frac{v^2}{r}$ , resulting in $8 ext{ m/s}^2$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of a car turning a sharp corner; you feel pushed outward because your body wants to go straight, while the centripetal force from the tires keeps the car moving in a circle.

🧠 Memory Mnemonic / Shortcut Aid

Remember 'AC' for 'Acceleration is Centripetal' calculated by 'v-squared over r'.

🔢 Key Formulas

$a_c = \frac{v^2}{r}$ — Formula for centripetal acceleration

$v = \omega r$ — Relationship between linear and angular velocity

⚙️ Working Principle

Centripetal acceleration is always directed towards the center of the circular path, perpendicular to the velocity vector. Because the direction of motion changes continuously even if speed remains constant, a net force must be acting toward the center, causing this constant centripetal acceleration.

📌 Key Points

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Centripetal acceleration is independent of the mass of the moving object.
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The acceleration vector points toward the center of the circle, while the velocity vector is tangent to the circle.
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Uniform circular motion implies constant speed but non-zero acceleration due to constant change in direction.

✅ Advantages

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Useful for calculating forces in mechanical systems like gears and turntables.

❌ Disadvantages / Limitations

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This formula is only valid for uniform circular motion; non-uniform motion requires tangential acceleration components.

🛠️ Applications / Uses

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Satellite orbital dynamics
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Banking of roads for vehicles

📄 Additional Information

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The given speed is $4 ext{ m/s}$ and radius is $2 ext{ m}$ . Calculation: $a_c = \frac{4^2}{2} = \frac{16}{2} = 8 ext{ m/s}^2$ .
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Option A is incorrect as it assumes simple division $4/2$ . Option B is incorrect as it ignores the squared term. Option D is incorrect as it uses $v^2$ without dividing by $r$ .

📊 Diagram / Illustration

✅

C is correct — The centripetal acceleration is calculated using the relation $a_c = \frac{v^2}{r}$ , which yields $8 ext{ m/s}^2$ .

Core Concepts Used

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Uniform Circular Motion Centripetal Acceleration Kinematics

💡 EXAM TIP

Always verify if the speed is given as linear speed (m/s) or angular velocity (rad/s), as the formula changes to $a_c = \omega^2 r$ for angular inputs.

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