AP Physics C Mechanics Questions on Centripetal Acceleration

📚 Quick Study Guide

• 🔄 Definition: Centripetal acceleration is the acceleration that causes an object to move in a circular path. It's always directed towards the center of the circle.
• 📐 Formula: The magnitude of centripetal acceleration ($a_c$) 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 crucial for understanding the forces involved.
• ⚖️ Centripetal Force: The net force causing the centripetal acceleration is called the centripetal force ($F_c$). Using Newton's second law, $F_c = ma_c = m\frac{v^2}{r}$.
• 🎢 Non-Constant Speed: If the speed is not constant, there's also tangential acceleration ($a_t$), tangent to the circular path. The total acceleration is then the vector sum of centripetal and tangential accelerations.

Practice Quiz

1. A car is moving around a circular track with a constant speed of 20 m/s. If the radius of the track is 100 m, what is the centripetal acceleration of the car?
   1. 0 m/s²
   2. 2 m/s²
   3. 4 m/s²
   4. 400 m/s²
2. A 2 kg mass is attached to a string and whirled in a horizontal circle of radius 1.5 m. If the mass completes 5 revolutions in 2 seconds, what is the centripetal force acting on the mass?
   1. 740 N
   2. 370 N
   3. 185 N
   4. 92.5 N
3. An object is moving in a circle of radius 4 m with a speed that is increasing at a rate of 2 m/s². At a certain instant, its speed is 6 m/s. What is the magnitude of the object's total acceleration at that instant?
   1. 2.25 m/s²
   2. 4.5 m/s²
   3. 2.5 m/s²
   4. 5.5 m/s²
4. A roller coaster car with a mass of 500 kg is at the bottom of a circular loop with a radius of 20 m. If the car's speed at the bottom is 15 m/s, what is the normal force exerted by the track on the car?
   1. 5625 N
   2. 3750 N
   3. 4900 N
   4. 8650 N
5. A satellite is orbiting the Earth in a circular orbit. If the orbital radius is doubled, by what factor does the centripetal acceleration change?
   1. 1/4
   2. 1/2
   3. 2
   4. 4
6. A ball is swung in a vertical circle at the end of a string. At which point in the circle is the tension in the string the greatest?
   1. At the top of the circle
   2. At the bottom of the circle
   3. At the sides of the circle (horizontal)
   4. Tension is constant throughout the circle
7. What happens to the centripetal acceleration if you double both the velocity and the radius of the circular path?
   1. It remains the same
   2. It doubles
   3. It quadruples
   4. It is halved