AP Physics 1: Simple Pendulum Multiple Choice Questions

📚 Quick Study Guide

• 📏 Definition: A simple pendulum consists of a mass (bob) suspended from a fixed point by a light string or rod.
• ⏱️ Period Formula: The period ($T$) of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity.
• ⚖️ Small Angle Approximation: The period formula is accurate for small angles (typically less than 15 degrees).
• ⚡ Factors Affecting Period: The period depends on the length of the pendulum and the acceleration due to gravity. It is independent of the mass of the bob.
• 🌍 Gravity's Role: On Earth, $g \approx 9.8 m/s^2$. Variations in $g$ can affect the pendulum's period.
• 🌱 Simple Harmonic Motion (SHM): For small angles, the motion of a simple pendulum approximates SHM.
• 💡 Energy Conservation: The total mechanical energy (potential + kinetic) of the pendulum is conserved if we neglect air resistance and friction.

Practice Quiz

1. A simple pendulum has a length of 1 meter. What is its approximate period on Earth?
   1. 2 seconds
   2. 4 seconds
   3. 1 second
   4. 6 seconds
2. If the length of a simple pendulum is doubled, what happens to its period?
   1. It is halved
   2. It is doubled
   3. It is multiplied by $\sqrt{2}$
   4. It remains the same
3. A pendulum is moved from Earth to the Moon, where the acceleration due to gravity is about 1/6 of Earth's. What happens to the pendulum's period?
   1. It decreases
   2. It increases
   3. It remains the same
   4. It becomes zero
4. Which of the following factors does NOT affect the period of a simple pendulum (assuming small angles)?
   1. Length of the pendulum
   2. Mass of the bob
   3. Acceleration due to gravity
   4. Amplitude of the swing (slightly)
5. For a simple pendulum undergoing SHM, at which point is the bob's speed the greatest?
   1. At the highest point of its swing
   2. At the lowest point of its swing
   3. Halfway between the highest and lowest points
   4. The speed is constant
6. A pendulum has a period of 2 seconds. If its length is increased by a factor of 4, what is the new period?
   1. 1 second
   2. 2 seconds
   3. 4 seconds
   4. 8 seconds
7. What happens to the period of a simple pendulum if the angle of swing is increased beyond the small angle approximation?
   1. The period decreases
   2. The period increases
   3. The period remains the same
   4. The period becomes zero