At theta = 0, which quantity is maximum?

At theta = 0, which quantity is maximum?

• A. Speed
• B. Potential energy
• C. Kinetic energy
• D. Restoring force

Answer: (C)

When the angle theta is zero, the pendulum is at the bottom of its swing. Here gravity has done its job of converting potential energy into motion, so the velocity is at its maximum. Kinetic energy depends on the square of that speed, so it reaches its largest value at this point. Potential energy, being tied to height, is at a minimum there, and the restoring force, which is proportional to sin theta, is zero when theta is zero. So among the quantities listed, the one that is largest is the kinetic energy, since it is directly tied to the maximum speed at this lowest point.

When the angle theta is zero, the pendulum is at the bottom of its swing. Here gravity has done its job of converting potential energy into motion, so the velocity is at its maximum. Kinetic energy depends on the square of that speed, so it reaches its largest value at this point. Potential energy, being tied to height, is at a minimum there, and the restoring force, which is proportional to sin theta, is zero when theta is zero. So among the quantities listed, the one that is largest is the kinetic energy, since it is directly tied to the maximum speed at this lowest point.