At theta = 0, bottom of the swing, which statement is true?

• A. F_restoring = 0; a_t = 0; U = 0; KE = max; v = max
• B. F_restoring = mg; a_t = 0; U = max; KE = 0; v = 0
• C. F_restoring = max; a_t = max; U = max; KE = max; v = max
• D. F_restoring = 0; a_t = max; U = 0; KE = 0; v = 0

Answer: (A)

At the bottom of the swing, gravity acts straight downward and the motion is along the arc. The tangential (restoring) component of gravity is proportional to sin theta, so when theta = 0 this component is zero. That means the restoring force along the swing is zero and the tangential acceleration is zero as well. With the height at its minimum, potential energy is at its lowest (zero if we set the bottom as the reference). Since energy is conserved, all of the energy is kinetic here, so the kinetic energy is at its maximum and the speed is greatest.

So the true statement is the one describing zero restoring force, zero tangential acceleration, minimum potential energy, and maximum kinetic energy and speed. The other descriptions contradict these geometric and energy facts—for example, implying a nonzero tangential force at the bottom or claiming potential energy is maximum, which would require inconsistent energy accounting.