2023 AP Physics 1 Free Response #5

Allen Tsao The STEM Coach
13 May 202307:52
EducationalLearning
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TLDRThe video discusses a 2023 AP Physics 1 free response problem involving a rod and sphere system rotating about a horizontal axle. The presenter analyzes angular acceleration, torque, and kinetic energy using frames from a student video. Key points include identifying the frame with the greatest angular acceleration, determining when the system has the highest rotational kinetic energy, and deriving an expression for the change in kinetic energy. The discussion emphasizes the role of gravitational force and torque in the system's motion, as well as the importance of energy conservation and the impact of external work when the Earth is excluded from the system.

Takeaways
  • ๐Ÿ“ The problem involves analyzing a rod-sphere system rotating around a horizontal axle due to a gravitational force.
  • ๐Ÿ” The sphere is lightly tapped, causing the system to rotate clockwise with negligible friction.
  • ๐ŸŽฅ The student uses video frames to analyze the motion, but the frames are not equally spaced in time.
  • โš™๏ธ The angular acceleration is greatest in frame C because the gravitational force is perpendicular to the R vector, resulting in the maximum torque.
  • ๐Ÿ”„ The rotational kinetic energy is highest in frame E when the system has the lowest gravitational potential energy.
  • ๐ŸŒ The problem assumes conservation of energy within the rod-sphere-Earth system, meaning no external work is done.
  • ๐Ÿงฎ The change in kinetic energy from frame A to frame E is calculated using the difference in gravitational potential energy, resulting in an expression of 3/2 mgl.
  • ๐Ÿ’ก The kinetic energy at the bottom is equal to the initial gravitational potential energy, minus zero initial kinetic energy.
  • โš–๏ธ When the Earth is not included in the system, gravity is considered an external force, and work done by gravity increases the kinetic energy.
  • ๐Ÿ› ๏ธ If the Earth is included, gravity is an internal force, allowing for the application of conservation of energy.
Q & A

  • What is the initial position of the rod-sphere system?

    -The rod-sphere system is initially balanced vertically upward on the axle.

  • What causes the rod-sphere system to rotate?

    -The rod-sphere system rotates clockwise due to a light tap and gravitational force.

  • What is the importance of figure two in the problem?

    -Figure two shows five frames of the rod-sphere system's rotation, which are used to answer the questions about angular acceleration and kinetic energy.

  • How do you determine when the angular acceleration of the rod-sphere system is the greatest?

    -Angular acceleration is greatest when the torque is greatest, which occurs when the gravitational force is perpendicular to the rod's axis of rotation, as seen in frame C.

  • What frame indicates the greatest rotational kinetic energy of the rod-sphere system?

    -Frame E indicates the greatest rotational kinetic energy because it is at the lowest potential energy point, thus having the highest kinetic energy due to conservation of energy.

  • How is the center of mass of the rod-sphere system described?

    -The center of mass is located three-quarters of the length (L) from the axis of rotation.

  • How do you derive the change in kinetic energy of the rod-sphere system?

    -The change in kinetic energy is derived by equating the potential energy at the top (initial) to the kinetic energy at the bottom (final), resulting in a change in kinetic energy of three-halves mgl.

  • Why does the rod and sphere gain kinetic energy even if the Earth is not included in the system?

    -If the Earth is not included, gravity becomes an external force doing work on the system, increasing its kinetic energy.

  • What happens to gravitational potential energy as the rod-sphere system rotates from vertical to horizontal?

    -Gravitational potential energy decreases, reaching its minimum when the system is at its lowest point, converting to maximum kinetic energy.

  • Why does frame C exhibit the greatest torque?

    -Frame C exhibits the greatest torque because the gravitational force is perpendicular to the rod, resulting in the maximum perpendicular distance (r) and thus the greatest torque.

Outlines
00:00
๐ŸŽ“ Overview of FRQ #5 Analysis

The video discusses the 2023 AP Physics 1 free-response question number 5. The speaker clarifies that solutions are not yet released and mentions that corrections will be noted if necessary. The problem involves a rod with a sphere attached, rotating due to gravitational force. The task is to analyze the rotation using video frames and determine the moments of greatest angular acceleration and kinetic energy. The explanation covers the importance of torque and rotational dynamics.

05:01
๐Ÿ“‰ Determining Changes in Kinetic Energy

The speaker delves into the change in kinetic energy of the rod-sphere system, starting from the initial position at frame A to the final position at frame E. They calculate the gravitational potential energy at the top and equate it to the kinetic energy at the bottom. The change in kinetic energy is derived as three halves mgl. The speaker also explains the effect of including or excluding the Earth in the system, clarifying that excluding it makes gravity an external force, thus performing work and increasing kinetic energy.

Mindmap
Keywords
๐Ÿ’กAngular acceleration
Angular acceleration refers to the rate at which the angular velocity of an object changes with time. In the video, it is discussed in the context of determining when the rod-sphere system experiences the greatest angular acceleration during its rotation. The concept is critical for understanding the dynamics of rotational motion and is related to the torque applied to the system.
๐Ÿ’กTorque
Torque is a measure of the force that can cause an object to rotate about an axis. In the video, the explanation of torque is linked to identifying the frame where the gravitational force exerts the greatest torque on the rod-sphere system. The torque is greatest when the force is perpendicular to the lever arm, which is explained using frame C from the video.
๐Ÿ’กFree body diagram
A free body diagram is a graphical representation used to visualize the forces acting on an object. In the video, the concept is mentioned in relation to analyzing the forces on the rod-sphere system to understand the dynamics of its motion. This diagram helps in identifying all the forces, including gravitational force and the force at the axle, contributing to the system's motion.
๐Ÿ’กKinematics
Kinematics is the branch of mechanics that describes the motion of objects without considering the forces causing the motion. In the video, kinematics is mentioned briefly as an alternative approach to understanding angular acceleration, although it is noted that there is not enough information to apply it in this scenario.
๐Ÿ’กConservation of energy
Conservation of energy is a fundamental principle stating that the total energy in an isolated system remains constant. The video explains how this principle applies to the rod-sphere system, where the total mechanical energy (potential + kinetic) is conserved as the system rotates from the top (maximum potential energy) to the bottom (maximum kinetic energy).
๐Ÿ’กRotational kinetic energy
Rotational kinetic energy is the energy due to the rotation of an object and is part of its total kinetic energy. In the video, it is discussed in the context of determining when the rod-sphere system has the greatest rotational kinetic energy, which occurs when the system is at its lowest potential energy (frame E).
๐Ÿ’กGravitational potential energy
Gravitational potential energy is the energy an object possesses because of its position in a gravitational field. The video uses this concept to explain the energy changes in the rod-sphere system as it rotates, with the potential energy being highest at the top and lowest at the bottom.
๐Ÿ’กAxis of rotation
The axis of rotation is the line about which an object rotates. In the video, the axis of rotation is the horizontal axle to which the rod is attached. Understanding this axis is crucial for analyzing the rotational motion and calculating the torque and angular acceleration of the system.
๐Ÿ’กMoment of inertia
Moment of inertia is a measure of an object's resistance to changes in its rotation. Although not explicitly detailed in the transcript, it is implied in the discussion of rotational dynamics, as it plays a key role in the equations governing angular acceleration (ฯ„ = Iฮฑ).
๐Ÿ’กWork done by gravity
Work done by gravity refers to the work performed by the gravitational force when an object moves in the direction of the force. The video explains that if the Earth is not included in the system, gravity does work on the rod-sphere system, increasing its kinetic energy. This is contrasted with the scenario where the Earth is included, making gravity an internal force with no work done.
Highlights

The problem involves a rod with a sphere attached to the end, rotating about a horizontal axle due to gravitational force.

The task is to determine when the angular acceleration of the rod system is the greatest.

Angular acceleration is greatest when the gravitational force is perpendicular to the rod, exerting the maximum torque.

Frame C is identified as the moment when the angular acceleration is the greatest because the gravitational force is perpendicular to the lever arm.

Torque is calculated using the formula: Torque = R ร— Force, where R is the distance from the axis of rotation to the point of force application.

The rotational kinetic energy of the rod-sphere system is greatest when it is spinning the fastest, which occurs at the lowest potential energy point.

Frame E is identified as having the greatest rotational kinetic energy because it is at the lowest point of potential energy.

Conservation of energy states that the total mechanical energy remains constant if no external work is done on the system.

The rod-sphere system has a mass m, length L, and the center of mass is located 3/4 of L from the axis.

The expression for the change in kinetic energy is derived from the gravitational potential energy difference as the system moves from the top to the bottom.

The initial gravitational potential energy is Mgh, where h is the vertical distance the center of mass moves, calculated as 3/2 L.

The change in kinetic energy from the top (frame A) to the bottom (frame E) is 3/2 mgl.

If the Earth is not included in the system, gravity acts as an external force, doing work and increasing the kinetic energy of the rod-sphere system.

When the Earth is included in the system, gravity is considered an internal force, and conservation of energy applies without external work.

The explanation highlights the difference between internal and external forces in energy conservation and how gravity's role changes based on system boundaries.

Transcripts

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PhysicsAP PhysicsFree ResponseAngular AccelerationTorqueKinetic EnergyGravitational ForceDynamicsConservation of EnergyEducational