![]() ![]() If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the Recall from Fixed-Axis Rotation on rotation that the net torque is equal to the moment of inertia I = ∫ r 2 d m I = ∫ r 2 d m times the angular acceleration α, α, where α = d 2 θ d t 2 α = d 2 θ d t 2: Like the simple pendulum, consider only small angles so that sin θ ≈ θ sin θ ≈ θ. To analyze the motion, start with the net torque. Here, the length L of the radius arm is the distance between the point of rotation and the CM. The magnitude of the torque is equal to the length of the radius arm times the tangential component of the force applied, | τ | = r F sin θ | τ | = r F sin θ. Recall that the torque is equal to τ → = r → × F → τ → = r → × F →. The minus sign is the result of the restoring force acting in the opposite direction of the increasing angle. ![]() Taking the counterclockwise direction to be positive, the component of the gravitational force that acts tangent to the motion is − m g sin θ − m g sin θ. When a physical pendulum is hanging from a point but is free to rotate, it rotates because of the torque applied at the CM, produced by the component of the object’s weight that acts tangent to the motion of the CM. The minus sign on the component of the weight that provides the restoring force is present because the force acts in the opposite direction of the increasing angle θ θ. The force of gravity acts on the center of mass (CM) and provides the restoring force that causes the object to oscillate. Consider an object of a generic shape as shown in Figure 15.21.įigure 15.21 A physical pendulum is any object that oscillates as a pendulum, but cannot be modeled as a point mass on a string. In the case of the physical pendulum, the force of gravity acts on the center of mass (CM) of an object. With the simple pendulum, the force of gravity acts on the center of the pendulum bob. A physical pendulum is any object whose oscillations are similar to those of the simple pendulum, but cannot be modeled as a point mass on a string, and the mass distribution must be included into the equation of motion.Īs for the simple pendulum, the restoring force of the physical pendulum is the force of gravity. We have described a simple pendulum as a point mass and a string. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out. Consider a coffee mug hanging on a hook in the pantry. Physical PendulumĪny object can oscillate like a pendulum. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12 ° 12 °. Pendulum 2 has a bob with a mass of 100 kg. Pendulum 1 has a bob with a mass of 10 kg. Each pendulum hovers 2 cm above the floor. Both are suspended from small wires secured to the ceiling of a room. ![]()
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