Centripetal Acceleration , Centripetal Force

Definition:

Centripetal acceleration is the acceleration of a particle moving in a circle, directed towards the center of the circle.

• Even if speed is constant, velocity changes because direction changes.

• Acceleration points toward the center (radially inward).

🔹 Formula:

ac=v2r=rω2a_c = \frac{v^2}{r} = r \omega^2ac=rv2=rω2

Where:

• vvv = linear speed along circular path

• rrr = radius of the circle

• ω\omegaω = angular speed (rad/s)

Key Points:

• SI unit = m/s²

• Direction = toward center

• Magnitude depends on speed and radius

🔵 2️⃣ Centripetal Force (FcF_cFc)

✅ Definition:

Centripetal force is the net force that keeps a body moving in a circular path, directed toward the center.

• Without this force, the body would move in a straight line (Newton’s first law).

• It is not a new kind of force — it can be tension, gravity, friction, or normal force.

🔹 Formula:

Fc=mac=mv2r=mrω2F_c = m a_c = \frac{m v^2}{r} = m r \omega^2Fc=mac=rmv2=mrω2

Where:

• mmm = mass of particle

• vvv = linear speed

• rrr = radius of circle

• ω\omegaω = angular speed

Key Points:

• SI unit = Newton (N)

• Points toward the center

• Acts perpendicular to motion, so no work is done by centripetal force

🔹 Examples

🔹 Important Tips

1. Centripetal acceleration depends on speed squared → faster = more acceleration.

2. Smaller radius → more acceleration and force needed.

3. Centripetal force is always toward the center.

4. Work done by centripetal force = 0 (perpendicular to motion).

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