• Understand that a force of constant magnitude always perpendicular to the velocity causes centripetal acceleration (12.2.1).
• Understand that centripetal acceleration produces circular motion at constant angular speed (12.2.2).
• Recall and use a = rω² and a = v²/r (12.2.3).
• Recall and use F = m r ω² and F = m v²/r (12.2.4).

• Use terms like centripetal acceleration, angular speed, tangential velocity correctly.
• Explain in English how a constant perpendicular force keeps an object in circular motion.
• Interpret and paraphrase technical definitions of circular motion concepts.

Centripetal acceleration: acceleration of an object moving in a circle, directed toward the center.

Centripetal force: net force causing centripetal acceleration, directed toward the center.

Angular speed (ω): rate of change of angle per unit time.

Tangential velocity (v): linear speed along the circular path.

When an object moves in a circle of radius r at constant speed, it experiences centripetal acceleration given by a = rω² or a = v²/r.
This arises from a net force F = m a always pointed toward the center.

In formula form:

a = rω²

a = v²/r

F = m r ω²

F = m v²/r

Key ideas:
– a perpendicularорталыққа бағытталған force
– constant angular speed
– uniform circular motion

1. Easy: Define centripetal acceleration in your own words.
2. Medium: Show algebraically how a = v²/r follows from a = rω², given v = rω.
3. Medium: Calculate the centripetal acceleration of a car going around a curve of radius 50 m at 20 m/s.
4. Hard (Critical): Discuss qualitatively what happens to the motion if the net force has even a small component tangential to the velocity.

1. What is the formula for centripetal acceleration in terms of angular speed?
   
   Answer

   a = rω²
2. Which force keeps an object moving in a circle?
   
   Answer

   Centripetal force
3. How is tangential velocity related to ω and r?
   
   Answer

   v = rω
4. What direction does centripetal acceleration point?
   
   Answer

   Toward the center of the circle
5. Write the expression for centripetal force using v and r.
   
   Answer

   F = m v²/r

**Related videos:**
— https://youtu.be/3A2dwgbL8vA
— https://youtu.be/Zn8I6f0qtoQ
— https://youtu.be/KAJsrh8Aves

**Tasks:**
1. Choose r = 0.5 m, set speed so that T = 2 s.
2. Record centripetal acceleration.
3. Compare with a = 4π²r/T².

1. Design a banked curve for a car traveling at 25 m/s on a radius of 80 m such that no friction is required. Find the banking angle.
2. Derive F = m v²/r starting from Newton’s second law and v = rω.
3. A satellite orbits Earth at 7.5 km/s at an altitude where r ≈ 7×10⁶ m. Calculate its centripetal acceleration.
4. Discuss qualitatively how non-uniform circular motion (speed changing) alters the net force direction and components.
5. Propose an experiment to measure centripetal force in a lab using a rotating platform and mass on string; outline procedure and expected errors.

• https://savemyexams.co.uk/as-a-level-physics–centripetal-motion/
• https://physicsandmathtutors.com/16-circular-motion/
• https://youtu.be/GvnSnh6ZLD4

• What concept about centripetal acceleration was most challenging?
• How would you explain the need for a net inward force to a peer?
• What real-world systems rely on centripetal force, and how?