AP Physics C Questions on Centripetal Acceleration: Exam Prep

📚 Quick Study Guide

• 🍎 Definition: Centripetal acceleration ($a_c$) is the acceleration that causes an object to move in a circular path. It always points towards the center of the circle.
• 📐 Formula: The magnitude of centripetal acceleration is given by $a_c = \frac{v^2}{r}$, where $v$ is the speed of the object and $r$ is the radius of the circular path.
• 🧭 Direction: The direction of centripetal acceleration is always towards the center of the circle. This is because it's the force constantly 'pulling' the object inward, changing its direction (but not its speed, for uniform circular motion).
• 💡 Key Points:
  • If the speed $v$ increases, the centripetal acceleration also increases (for a constant radius).
  • If the radius $r$ increases, the centripetal acceleration decreases (for a constant speed).
• 📝 Relationship with Force: Centripetal acceleration is caused by a centripetal force ($F_c$), given by $F_c = ma_c = \frac{mv^2}{r}$, where $m$ is the mass of the object.

🧪 Practice Quiz

1. A car is moving at a constant speed of 20 m/s around a circular track with a radius of 100 m. What is the magnitude of the car's centripetal acceleration?
   1. 0 m/s²
   2. 2 m/s²
   3. 4 m/s²
   4. 20 m/s²
2. A particle is traveling in a circle of radius 5 m with a speed of 10 m/s. What is the centripetal acceleration of the particle?
   1. 5 m/s²
   2. 10 m/s²
   3. 20 m/s²
   4. 40 m/s²
3. If the radius of a circular path is doubled, and the speed remains constant, what happens to the centripetal acceleration?
   1. It doubles.
   2. It quadruples.
   3. It halves.
   4. It remains the same.
4. An object is moving in a circle with a constant speed. If the centripetal acceleration is 8 m/s² and the radius is 2 m, what is the speed of the object?
   1. 2 m/s
   2. 4 m/s
   3. 8 m/s
   4. 16 m/s
5. A 2 kg mass is moving in a circle of radius 3 m with a speed of 6 m/s. What is the centripetal force acting on the mass?
   1. 4 N
   2. 12 N
   3. 24 N
   4. 36 N
6. A ball is swung in a horizontal circle at the end of a 1.5 m string. If the ball's speed is 4 m/s, what is its centripetal acceleration?
   1. 2.67 m/s²
   2. 6 m/s²
   3. 10.67 m/s²
   4. 16 m/s²
7. A race car is traveling around a circular track. If the car's speed is doubled, how does the centripetal acceleration change?
   1. It remains the same.
   2. It doubles.
   3. It quadruples.
   4. It halves.