2017 AP Physics 1 Free Response #3
TLDRIn this educational video, Alan from Bottle Stem Coach tackles AP Physics 1 free response question 2017, number 3. He discusses the concept of angular momentum and torque in the context of a rod with a pivot point, impacted by a sliding disc. Alan explains why hitting the rod further to the right increases torque and thus angular speed. He critiques incorrect equations for post-collision angular speed, emphasizing the importance of mass and rotational inertia. Finally, he uses conservation of angular momentum to derive the correct equation for the rod's post-collision speed, comparing it to scenarios where the disc bounces off.
Takeaways
- π The video is a continuation of the analysis of the 2017 AP Physics 1 free response questions, focusing on question number three.
- ποΈ The scenario involves a rod of length 'D' with a pivot at point 'C', initially at rest, and a student sliding a disc of mass 'm' towards the rod, which will stick to it at a distance 'X' from the pivot.
- π The goal is to give the rod the maximum possible angular speed by determining the optimal position to strike the rod with the disc.
- π The student's reasoning suggests that striking the rod further to the right of point 'C' will result in more torque, and hence a higher angular speed due to the increased moment arm.
- 𧩠An equation for post-collision angular speed, Omega, is presented, and its agreement with the qualitative reasoning is confirmed, showing that Omega increases with larger 'X'.
- β The video identifies a mistake in an alternative equation for Omega, noting that it does not make physical sense due to the incorrect placement of the mass of the disc 'M' in the denominator.
- π The video explains that the mass of the disc should increase the angular speed, not decrease it, as it would exert a greater force on the rod.
- π The video also points out another mistake in the equation regarding the rotational inertia 'I', which should be in the denominator to reflect its effect on making the system harder to rotate.
- π In part D, the video uses the conservation of angular momentum to derive an equation for the post-collision angular speed of the rod, considering the combined rotational inertia of the rod and the disc.
- π The video discusses a scenario where the disc bounces off the rod instead of sticking to it, and explains that the post-collision angular speed of the rod would be greater due to the conservation of angular momentum and the reduced rotational inertia.
- π The video concludes with a summary of the scoring guidelines for the question, highlighting the importance of understanding torque, angular momentum, and their implications in physics problems.
Q & A
What is the main topic of the video?
-The main topic of the video is the analysis of the 2017 AP Physics 1 free response question number three, which involves a rod with a disc sliding towards it and the principles of angular momentum and torque.
What is the physical setup described in the problem?
-The physical setup involves a rod of length 'd' with a rotational inertia 'I', pivoted at a frictionless horizontal surface at point 'C', which is the center of the rod. A student slides a disc of mass 'm' towards the rod with a velocity perpendicular to the rod, and the disc sticks to the rod at a distance 'x' from the pivot.
What is the goal of the student in the problem?
-The goal of the student is to give the rod as much angular speed as possible by sliding the disc towards the rod.
Why should the disc hit the rod to the right of point C to maximize angular speed?
-Hitting the rod to the right of point C maximizes the torque, which is the product of force and distance from the pivot. The greater the torque, the more angular speed the rod can achieve.
What is the relationship between the position 'x' and the angular speed 'Omega' of the rod?
-As 'x' increases, the angular speed 'Omega' of the rod also increases because a larger 'x' results in a larger torque, which in turn imparts more angular speed to the rod.
What is the issue with the equation for post-collision angular speed 'Omega' found on the internet?
-The equation does not make physical sense because it incorrectly suggests that increasing the mass of the disc (M_disk) would decrease the angular speed 'Omega', which contradicts the expected physical behavior.
Why is the mass of the disc (M_disk) incorrectly placed in the denominator in the equation?
-The mass of the disc should increase the angular speed 'Omega' because a more massive disc would exert a greater force on the rod, thus increasing its angular speed. Placing M_disk in the denominator contradicts this expected behavior.
What is the correct approach to determine the post-collision angular speed 'Omega' of the rod?
-The correct approach is to use the conservation of angular momentum. The initial angular momentum of the disc is equal to the final angular momentum of the combined system of the rod and the disc after the collision.
How does the rotational inertia 'I' affect the post-collision angular speed 'Omega'?
-A larger rotational inertia 'I' makes it harder to rotate the system, so as 'I' increases, the angular speed 'Omega' should decrease, assuming the same amount of angular momentum is conserved.
What happens if the disc bounces off the rod instead of sticking to it?
-If the disc bounces off, the post-collision angular speed of the rod would be greater than if the disc stuck to the rod. This is because the net angular momentum is the same, but the rotational inertia of the rod alone is less than that of the rod plus the disc, resulting in a higher 'Omega'.
What is the significance of angular momentum conservation in this problem?
-The conservation of angular momentum is crucial in determining the post-collision angular speed of the rod. It ensures that the total angular momentum before and after the collision remains constant, allowing us to calculate the final state of the system.
Outlines
π§ Physics Problem Analysis: Rod and Disc Collision
In this paragraph, Alan discusses a physics problem involving a rod of length 'D' with a rotational inertia 'I', pivoted at a frictionless horizontal surface. A disc of mass 'm' is slid towards the rod with a velocity perpendicular to the rod, sticking at a distance 'x' from the pivot. The goal is to maximize the rod's angular speed. Alan explains that the torque, and thus the angular speed, is maximized when the disc hits the rod further to the right of point 'C'. He also critiques an equation found online, pointing out that it does not make physical sense due to the incorrect dependence on the mass of the disc and the rotational inertia of the rod.
π Deriving Angular Speed Post Collision
Alan continues by explaining the conservation of angular momentum in the system. He derives an equation for the post-collision angular speed 'Omega' of the rod, considering the combined rotational inertia of the rod and the disc. He emphasizes that the angular momentum before and after the collision must be equal, leading to the equation 'Omega = M_disk * V_nought * x / (I_rod + M_disk * x^2)'. Alan then discusses a scenario where the disc bounces off the rod instead of sticking to it, explaining that the post-collision angular speed of the rod would be greater due to the conservation of angular momentum and the reduced rotational inertia.
π AP Physics 1 Free Response Question Review
In the final paragraph, Alan reviews the scoring guidelines for the AP Physics 1 free response question, providing insights into the correct and incorrect answers for the given problem. He confirms that the correct answers involve understanding torque, angular momentum, and the effects of the disc's mass and position on the rod's angular speed. Alan concludes by acknowledging the complexity of angular momentum in AP Physics 1 and encourages viewers to engage with the content by leaving comments, likes, or subscribing for more free response questions.
Mindmap
Keywords
π‘Angular Speed
π‘Torque
π‘Rotational Inertia
π‘Pivot
π‘Collision
π‘Angular Momentum
π‘Impulse
π‘Disc
π‘Derive
π‘Conservation Laws
π‘Bouncing Off
Highlights
Alan from Bottle Stem is discussing AP Physics 1 free response questions for the year 2017.
The analysis focuses on question number three, involving a rod with a pivot and a disc's impact on its rotation.
The rod's left end is attached to a frictionless horizontal service, with a pivot above point C marking the center.
The rod is initially motionless but can rotate around the pivot, simulating a swinging motion.
A student slides a disc of mass m towards the rod, which sticks to the rod at a distance x from the pivot.
The goal is to maximize the rod's angular speed by sliding the disc with a specific velocity.
The rod is assumed to be significantly more massive than the disc for simplification.
Torque is discussed as a factor in increasing the rod's angular speed, with distance from the pivot being crucial.
An equation for post-collision angular speed, Omega, is presented, and its correctness is questioned.
Qualitative reasoning suggests that increasing x should increase Omega, which aligns with the equation's form.
A mistake in deriving the equation for Omega is identified, with the mass of the disk (M_disk) incorrectly placed in the denominator.
The velocity of the disc and its distance from the pivot are correctly identified as factors increasing Omega.
The rotational inertia (I) of the rod is discussed, with its impact on the ease of rotation and Omega.
A correct equation for Omega is derived using conservation of angular momentum principles.
The scenario where the disc bounces off the rod instead of sticking is considered, affecting Omega.
The post-collision angular speed of the rod is expected to be greater when the disc bounces off due to conservation of angular momentum and reduced rotational inertia.
Scoring guidelines for the question are briefly mentioned, emphasizing the importance of understanding torque and angular momentum.
The video concludes with a call to action for viewers to comment, like, or subscribe for more informative content.
Transcripts
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