Allen Tsao The STEM Coach

29 Aug 201809:23

EducationalLearning

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TLDRIn this educational video, Alan from Bothell STEM Coach explains AP Physics 1, focusing on the 2018 free response question three. He discusses the physics of a spinning disk with frictional torque, leading to a constant angular acceleration until the disk comes to rest. Alan sketches graphs of angular velocity and acceleration over time, deriving equations for rotational inertia and analyzing the effect of applying oil to reduce friction. He concludes by comparing two mathematical models for the torque exerted by the axle, correctly identifying the model that represents the decreasing torque over time.

###### Takeaways

- 📚 Alan is teaching AP Physics 1, focusing on the 2018 free response question number three.
- 🔧 The problem involves a spinning disk with friction between the axle and the disc, which exerts a constant torque.
- 📉 The initial angular velocity of the disk is positive and counterclockwise, denoted as Omega naught.
- 🛑 The disk comes to rest at a later time, T equals t1.
- 📈 Alan instructs to sketch a graph of the disk's angular velocity as a function of time until it comes to rest.
- 🔄 The relationship between torque and angular acceleration is given by torque equals the moment of inertia times angular acceleration.
- 🔢 The angular acceleration is constant and negative, calculated as negative tau over I.
- 📉 The graph of angular velocity should be a straight line with a negative slope, indicating a decrease to rest.
- ⚙️ The moment of inertia I can be derived from the equation I equals tau over alpha, where alpha is the negative angular acceleration.
- 🛠️ In a follow-up experiment, dripping oil reduces the friction, leading to a decrease in torque and thus a change in the graph's behavior.
- 📊 The graph for the second experiment should show a decrease in angular velocity that doesn't reach zero within the given time frame due to reduced friction.
- 📝 Alan evaluates two mathematical models for the torque exerted by the axle and concludes that the model where torque decreases over time is correct.

###### Q & A

### What is the topic of the video presented by Alan?

-The video is about continuing the AP Physics 1 2018 free response question number three.

### What is the physical scenario described in the video?

-The scenario involves a disk that spins about an axle at its center with friction between the axle and the disk exerting a constant torque, causing the disk to eventually come to rest.

### What is the initial angular velocity of the disk at time T equals zero?

-The initial angular velocity of the disk is positive and is denoted as Omega naught.

### What is the relationship between torque and angular acceleration as described in the video?

-The relationship is given by the equation torque equals moment of inertia times angular acceleration, where the moment of inertia (I) is a property of the disk.

### Why is the angular acceleration considered to be constant in the video?

-The angular acceleration is considered constant because the torque exerted by the friction is constant, and thus, according to the relationship between torque and angular acceleration, the acceleration must also be constant.

### How does the video describe the graph of the disk's angular velocity as a function of time?

-The graph is described as a straight line starting from the initial angular velocity Omega naught and decreasing linearly until it comes to rest at time T equals t1.

### What is the equation for the disk's angular velocity in terms of time as per the video?

-The equation is Omega = Omega naught + alpha * T, which is the angular velocity version of the kinematic equation for linear motion.

### How does the video explain deriving the equation for the rotational inertia (I) of the disk?

-The video explains that I can be derived from the equation I = torque / angular acceleration, and further elaborates on how to find the angular acceleration from the change in angular velocity over time.

### What changes occur in the second experiment when oil is dripped on the contact surface?

-In the second experiment, as oil is dripped on the contact surface, the friction, and consequently the torque, decreases over time, which affects the angular acceleration and the graph of angular velocity versus time.

### What is the correct mathematical model for the torque exerted by the axle on the disk when oil is present, according to the video?

-The correct model is the one where the torque decreases over time, as friction is reduced by the oil, which is represented by the equation where torque is equal to a decreasing function of time.

### How does the video conclude about the scoring for the question?

-The video concludes that all points for the question were correctly earned, with a brief mention of the importance of including the negative sign in the equation for rotational inertia.

###### Outlines

00:00

##### 📚 AP Physics 1: Analyzing Frictional Torque and Angular Motion

In this educational video, Alan from Bothell STEMcoach discusses AP Physics 1, specifically focusing on the 2018 free response question number three. The scenario involves a spinning disk with frictional torque exerted by an axle, leading to a constant angular deceleration until the disk comes to rest. Alan explains the relationship between torque, moment of inertia, and angular acceleration, emphasizing that with a constant torque, the angular acceleration must also be constant. He guides viewers through the process of sketching graphs for angular velocity and acceleration, illustrating how the disk's motion can be represented over time. The video also covers deriving an equation for the rotational inertia of the disk in terms of given parameters, such as the initial angular velocity, torque, and time to rest.

05:01

##### 🛠️ Experiment with Friction Reduction Using Oil

The second paragraph of the video script delves into a follow-up experiment where oil is applied to reduce friction between the axle and the spinning disk. As the friction decreases, the torque exerted by the axle also diminishes, leading to a reduction in the disk's angular acceleration. Alan sketches a graph to represent the change in angular velocity over time, suggesting that the acceleration curve will decrease as friction is reduced. He discusses the student's attempt to model the torque over time with two equations, one suggesting an increase and the other a decrease in torque. Alan concludes that the equation where torque decreases over time is the correct model for this experiment, aligning with the observed reduction in friction. The video ends with a quick review of the scoring for the question and an invitation for viewers to check the solution keys on the website, encouraging comments, likes, or subscriptions for further educational content.

###### Mindmap

###### Keywords

##### 💡AP Physics 1

AP Physics 1 is a college-level course and examination offered by the College Board as part of the Advanced Placement Program. It is designed to provide students with a foundational understanding of physics concepts. In the video, the theme revolves around solving a free response question from the 2018 AP Physics 1 exam, which is a significant part of the educational content.

##### 💡Free Response Question

In the context of AP exams, a free response question is an open-ended problem that requires students to provide a detailed answer, often involving calculations or explanations. The video focuses on question number three of the 2018 AP Physics 1 exam, which is a free response type, requiring the application of physics principles to solve.

##### 💡Torque

Torque is a measure of the force that can cause an object to rotate about an axis. It is a vector quantity and is calculated as the cross product of the radius vector and the force vector. In the video, torque is discussed in relation to the friction between the axle and the disc, which exerts a constant torque on the spinning disk.

##### 💡Angular Velocity

Angular velocity is the rate of change of an angle with respect to time and is a vector quantity that represents how fast an object is rotating. In the video, the initial counter-clockwise angular velocity of the disk is denoted as Omega naught, and the problem involves sketching a graph of angular velocity as a function of time until the disk comes to rest.

##### 💡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 is used in the formula relating torque and angular acceleration. The video explains that if the torque is constant, the angular acceleration must also be constant, indicating the disk's rotational inertia.

##### 💡Friction

Friction is the force that resists the relative motion of two surfaces in contact. In the context of the video, friction between the axle and the disc is responsible for the constant torque acting on the spinning disk, which ultimately brings the disk to rest.

##### 💡Graph

A graph is a visual representation of data, typically involving a set of axes representing variables. In the video, the task is to sketch graphs representing the disk's angular velocity and angular acceleration as functions of time, which helps visualize the physical behavior of the system.

##### 💡Kinematic Equation

Kinematic equations relate the motion of an object to its initial conditions and the forces acting upon it. In the video, the angular velocity equation, which is the rotational equivalent of the linear kinematic equation, is used to describe the change in angular velocity over time due to constant angular acceleration.

##### 💡Oil

In the second part of the video, oil is introduced to the contact surface between the axle and the disc to reduce friction. This action changes the torque exerted on the disc over time, which is then reflected in the graph of angular velocity as a function of time.

##### 💡Constant

In the context of the video, a constant refers to a value that does not change over time. The video mentions a constant torque exerted by the frictional force at the beginning and later discusses how the introduction of oil changes this scenario, leading to a non-constant torque.

##### 💡Acceleration

Acceleration is the rate of change of velocity over time. In the video, angular acceleration is discussed as the constant rate of change of angular velocity, which is represented by the slope of the graph for the disk's motion. The reduction of friction due to oil application affects this acceleration, causing it to decrease over time.

###### Highlights

Alan introduces the AP Physics 1 2018 free response question number three.

The disk spins around an axle with friction between them, exerting a constant torque.

At time T equals zero, the disk has an initial counter clockwise angular velocity.

Students are asked to sketch a graph of the disk's angular velocity over time until it comes to rest.

The relationship between torque and angular acceleration is discussed, with torque being constant.

The angular acceleration is negative and constant, indicating the disk is slowing down.

The magnitude of the frictional torque is derived using the equation tau equals negative tau over I.

An equation for the rotational inertia I of the disk is derived in terms of given variables.

The acceleration is the slope of the angular velocity graph, which is negative due to the disk slowing down.

The torque exerted on the disk decreases as oil is dripped on the axle-disc contact surface.

A new graph is sketched to represent the disk's angular velocity as friction is reduced by oil.

The torque decreases over time as more oil reaches the contact surface.

Two equations are presented to model the torque over time, with one being correct.

Equation two is identified as the correct model, showing torque decreasing over time.

The scoring criteria for the question are briefly reviewed, ensuring all points are covered.

A summary of the solution process is provided for review and understanding.

Alan encourages viewers to check the solution key on the website for further review.

The video concludes with a prompt for comments, likes, or subscriptions for the next video.

###### Transcripts

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AP PhysicsFriction StudyTorque AnalysisAngular VelocityRotational InertiaKinematic EquationsEducational VideoPhysics ExperimentBothell StemAlan Coach