2018 #3 Free Response Question - AP Physics 1 - Exam Solution

Flipping Physics
22 Apr 202010:19
EducationalLearning
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TLDRIn this instructional video, students delve into a physics problem involving a spinning disk subjected to frictional torque. The scenario from the 2018 AP Physics 1 exam requires the students to sketch graphs of the disk's angular velocity and acceleration over time, first without and then with the introduction of oil to reduce friction. The problem culminates in evaluating two mathematical models for the torque exerted by the axle on the disk in the presence of oil, with the correct model demonstrating a decreasing torque over time.

Takeaways
  • 📝 The problem discussed is a free response question from the 2018 AP Physics 1 exam involving the analysis of a spinning disk subjected to frictional torque.
  • ⏱ Part A asks for graphical representations of the disk's angular velocity and acceleration over time, from the start until the disk comes to rest.
  • 📉 The angular velocity graph should show a straight line with a constant negative slope, starting from an initial angular velocity (ω₀) and ending at zero.
  • 🔽 The acceleration graph should feature a horizontal line below the x-axis, indicating a constant negative angular acceleration.
  • 🌟 Emphasis is placed on the importance of accurate graph drawing, as it constitutes a significant portion of the question's points.
  • 🔧 In Part B, the goal is to derive an equation for the rotational inertia (I) of the disk using given parameters and physical constants.
  • 🔄 The net torque on the disk is equal to the frictional torque, which is constant, and is opposed to the direction of the disk's spin.
  • 📌 Angular acceleration (α) is defined as the change in angular velocity (Δω) over the change in time (Δt), calculated as -ω₀/t₁.
  • 🚫 Part C introduces an experiment where oil is applied to reduce friction, affecting the disk's angular velocity and acceleration graphs from t = 0 to t = t₁.
  • 📉 The second half of the angular velocity graph should become flatter, indicating a decreasing angular acceleration due to reduced friction.
  • 🔄 For Part D, two equations are proposed to model the torque exerted by the axle on the disk when oil is present. Only one of the equations is plausible based on the expected behavior of torque.
  • 💡 Equation 2 (τ = c₂ / (t + 1/2t₁)) is selected as the better model because it aligns with the expected decrease in torque as time increases, unlike Equation 1.
Q & A

  • What is the scenario described in the 2018 AP Physics 1 exam free response question number three?

    -The scenario involves a disk spinning about an axle and experiencing a constant torque due to friction between the axle and the disc, which eventually brings the disk to rest.

  • How does the angular velocity of the disk change over time when it starts to spin?

    -The angular velocity of the disk changes linearly with a constant negative slope from its initial value (omega not) to zero as it comes to rest at time t equals t1.

  • What is the relationship between the frictional torque and the angular acceleration of the disk?

    -The frictional torque causes a constant negative angular acceleration, which is the rate of change of the angular velocity over time.

  • How is the rotational inertia of the disk derived in Part B of the problem?

    -The rotational inertia (I) of the disk is derived using the equation I = tau not * t1 / omega not, where tau not is the frictional torque, t1 is the time it takes for the disk to come to rest, and omega not is the initial angular velocity.

  • What happens to the friction between the axle and the disc during the second part of the experiment in Part C?

    -In Part C, oil is applied to the contact surface between the axle and the disc, which gradually reduces the friction and subsequently the net torque and angular acceleration of the disk.

  • How does the graph of the disk's angular velocity change in the second half of the experiment?

    -In the second half, the graph of the angular velocity becomes flatter, indicating a decreasing angular acceleration due to the reduced friction from the oil application.

  • What is the significance of the two equations provided in Part D for modeling the torque exerted by the axle on the disk when oil is present?

    -The two equations in Part D attempt to mathematically model the changing torque due to the presence of oil. One suggests an increasing torque with time, while the other suggests a decreasing torque. The latter is more plausible as it aligns with the expected decrease in friction due to oil application.

  • Which equation is chosen as the better model for the experiment in Part D, and why?

    -Equation 2 (torque equals constant 2 divided by the quantity time plus one half time one) is chosen as the better model because it correctly represents the decreasing torque due to the oil application, unlike equation 1 which incorrectly suggests an increasing torque.

  • What is the importance of the graphs in this physics problem?

    -The graphs are crucial for visualizing the changes in angular velocity and acceleration over time. They help in understanding the physical behavior of the disk under different conditions and are worth a significant portion of the points in the exam question.

  • How does the presence of oil affect the angular acceleration graph in Part C?

    -The presence of oil reduces the friction, leading to a decrease in the net torque and thus the angular acceleration. This is represented by a curved line in the angular acceleration graph, moving towards the horizontal axis in the second half, indicating a decreasing acceleration.

  • What is the role of angular acceleration in determining the slope of the angular velocity graph?

    -The slope of the angular velocity graph is directly related to the angular acceleration. A constant angular acceleration results in a straight line slope on the graph, while a changing angular acceleration, as in the case with oil application, results in a curved slope that flattens over time.

Outlines
00:00
📈 Free Response Question Analysis

The paragraph discusses the analysis of a free response question from the 2018 AP Physics 1 exam. It involves a problem about a spinning disk that experiences frictional torque, leading to a change in its angular velocity and acceleration over time. The students, Billy and Bobby, are tasked with sketching graphs of the disk's angular velocity and acceleration as functions of time, and solving for the rotational inertia of the disk. The paragraph emphasizes the importance of accurately drawing these graphs and understanding the physics concepts behind the problem, such as constant torque leading to constant negative angular acceleration, and how the introduction of oil affects the friction and subsequent motion of the disk.

05:01
🔧 Experiment with Reduced Friction

This paragraph continues the discussion on the physics problem, focusing on a second scenario where oil is introduced to reduce friction between the axle and the disc. The students are asked to sketch new graphs representing the changes in the disk's angular velocity and acceleration over time as the friction decreases. The summary explains that the first half of the graphs should match the previous scenario, while the second half will show a decreasing angular acceleration due to reduced friction. The paragraph highlights the importance of careful graph drawing and understanding the impact of changing physical conditions on the motion of the disk.

10:04
📊 Torque Modeling with Oil

The final paragraph of the script addresses the student's attempt to mathematically model the torque exerted on the disk when oil is present. Two equations are proposed, and the students must determine which one better represents the experimental data. The analysis involves substituting specific time values into the equations to evaluate the torque and deduce that the second equation, which models a decreasing torque over time, is more plausible. This paragraph emphasizes the importance of accurate mathematical modeling and the ability to apply physical laws to real-world scenarios.

Mindmap
Keywords
💡Angular Velocity
Angular velocity is a measure of how quickly an object rotates or spins around a specific axis. It is defined as the rate of change of the angle with respect to time. In the context of the video, the disk's initial angular velocity is given as positive (counterclockwise) and it decreases to zero as the disk comes to rest. The graph of angular velocity versus time is a straight line with a negative slope, indicating a constant deceleration due to friction.
💡Torque
Torque is a measure of the force's tendency to cause or change the rotational motion of an object. It is a vector quantity that depends on the magnitude of the force, the distance from the axis of rotation, and the direction of the force. In the video, friction between the axle and the disk exerts a constant torque on the disk, causing it to slow down and eventually stop.
💡Friction
Friction is a force that opposes the relative motion or tendency of such motion of two surfaces in contact. In the context of the video, friction between the axle and the disk is the only force causing a torque, leading to the disk's deceleration. The introduction of oil in later parts of the experiment reduces friction, altering the torque and the disk's rotational behavior.
💡Acceleration
Acceleration is the rate of change of velocity of an object with respect to time. In the context of the video, angular acceleration refers to the rate at which the angular velocity of the disk changes. The disk experiences a constant negative angular acceleration due to the frictional torque, which is represented by a horizontal line below the x-axis in the graph.
💡Rotational Inertia
Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotation. It depends on the mass distribution of the object and its shape. In the video, the rotational inertia of the disk is derived using the given values of torque, initial angular velocity, and time it takes for the disk to stop.
💡Graphs
Graphs are visual representations of data or functions, showing the relationship between variables. In the video, graphs are used to represent the disk's angular velocity and acceleration as functions of time. Properly drawing and interpreting these graphs is crucial for solving the physics problem presented.
💡Deceleration
Deceleration is the decrease in speed or velocity of an object. In the context of the video, the disk experiences deceleration due to the constant torque applied by friction, which causes it to slow down from its initial angular velocity to a final velocity of zero.
💡Oil
In the video, oil is introduced to the contact surface between the axle and the disk to reduce friction. As more oil is applied, the frictional force decreases, which in turn reduces the torque and alters the disk's angular acceleration, leading to a change in the shape of the graphs representing the disk's motion.
💡Equations
Equations are mathematical statements that assert the equality of two expressions. In the context of the video, equations are used to model the torque exerted by the axle on the disk when oil is present. The student must determine which equation best fits the experimental data.
💡Constant
A constant is a value that does not change. In the video, certain physical quantities such as the frictional torque and the initial angular velocity are described as constants because they remain the same throughout the process of the disk slowing down.
Highlights

The problem discussed is from the 2018 AP Physics 1 exam, focusing on the rotational dynamics of a spinning disk under the influence of friction.

Friction between the axle and the disk exerts a constant torque on the disk, causing it to slow down and eventually stop.

The angular velocity of the disk is represented as a function of time, starting with an initial positive value and decreasing linearly to zero.

The angular acceleration of the disk is constant and negative, represented by a horizontal line below the x-axis on the acceleration graph.

Part A of the question emphasizes the importance of graphing, which accounts for one-third of the total points for this question.

The rotational inertia of the disk is derived using the equation I = τ_not * t_1 / ω_not, where τ_not is the frictional torque, t_1 is the time to stop, and ω_not is the initial angular velocity.

In Part C, the introduction of oil between the axle and the disk reduces friction, altering the torque and angular acceleration over time.

The first half of the angular velocity and acceleration graphs in Part C remain the same as in Part A until the oil starts to affect the system.

The second half of the angular acceleration graph in Part C shows a decrease in magnitude, indicating a reduction in the net torque due to the oil.

The angular velocity graph in Part C shows a flatter slope in the second half, indicating a decreasing rate of deceleration.

Part D involves mathematically modeling the torque exerted by the axle on the disk when oil is present, using two different equations.

Equation 1 suggests a torque that starts at zero and increases, which is not plausible as the torque should decrease over time.

Equation 2 models a torque that starts at a positive value and decreases, which is plausible and better represents the experimental scenario.

The importance of accurate graphing is reiterated, with the four graphs in question three accounting for eight out of twelve points.

The problem-solving process involves understanding the relationship between torque, angular velocity, and angular acceleration in a physical system.

The practical application of this problem is in understanding how external factors, such as oil, can affect the dynamics of a rotating system.

The problem highlights the importance of visual representation of data through graphs in physics, as they provide a clear and concise way to understand complex phenomena.

The use of equations to model real-world scenarios is a fundamental aspect of physics, allowing for predictions and analysis of system behavior.

The transcript serves as an educational tool, demonstrating the process of solving physics problems and the critical thinking involved.

Transcripts

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