10.2.2 Physical Pendulums Flashcards
Physical Pendulums
- Most real-world pendulums are extended objects, not point masses on ideal strings. These pendulums are called physical pendulums.
- The differential equation describing physical pendulums is . Since this equation has the same form as the differential equation describing simple harmonic motion, physical pendulums execute SHM.
- Whenever a system’s motion is described by a differential equation of the form , that system executes SHM.
A particular pendulum consists of a thin plywood disk of mass m and radius r pivoted about a point along its edge. If one were to use the equation for the period of a simple pendulum, which of the following would be the fractional error?
sqrt(3/2)
An astronaut sets up a physical pendulum on the Moon, where the acceleration of gravity is g / 6. The pendulum’s length is 2.00 m and timing begins as it passes through its equilibrium position. The astronaut initially displaces the pendulum 0.1 radians. Which of the following is the equation for the pendulum’s acceleration as a function of time?
a(t) = -0.1(g/8l) * cos (sqrt(g/8l)t + pi/2)
At an airport, an early biplane is suspended from the celing by a cable attached to the propeller end and a ring hooked through the tail end. Suppose that one of the cables breaks, causing the biplane to swing in simple harmonic motion about the tail after a few minutes of chaos. Which of the following factors has the largest effect on the period of this physical pendulum?
The engine is removed, reducing the mass of the propeller end of the plane.
A kitten plays with a dangling hollow spherical glass ornament. When she gives the ornament a 0.2-radian nudge, the ball begins to oscillate with SHM. Which of the following is the equation for the angular position of the ornament as a function of time? The moment of inertia of a sphere about its center of mass is I = (2/3)mr^2
theta(t) = 0.2 cos(sqrt(3g/5r)t)
