A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 2.46 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 2.90 N of constant tension to each string. If it T takes 0.770 s for the string to unwind, how much angular momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R P h kg-m? L = S Incorrect
A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 2.46 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 2.90 N of constant tension to each string. If it T takes 0.770 s for the string to unwind, how much angular momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R P h kg-m? L = S Incorrect
A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 2.46 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 2.90 N of constant tension to each string. If it T takes 0.770 s for the string to unwind, how much angular momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R P h kg-m? L = S Incorrect
Transcribed Image Text:**Diagram Explanation**
This educational diagram depicts a child's top set up on a frictionless surface. The diagram labels several parts of the top and illustrates the forces acting upon it:
- **Axle**: The top has an axle with a radius of \( r = 2.46 \, \text{mm} \). This is where two strings are wrapped around.
- **Tension Force (T)**: Two arrows labeled \( T \) point outward, indicating the constant tension of \( T = 2.90 \, \text{N} \) applied to each string.
- **Diameter of Axle**: The distance marked \( 2r \) is the diameter of the axle, which is twice the radius.
- **Point P**: Located on the surface of the conical part of the top, representing a point where the radius \( R \) and height \( h \) intersect.
- **Angle \(\theta\)**: Indicates the angle of elevation from the base to Point P.
- **Height (\( h \))**: Represents the vertical distance from the base to the top of the conical part.
**Problem Description**
A child's top is held in place upright on a frictionless surface. The axle has a radius of \( r = 2.46 \, \text{mm} \). Two strings are wrapped around the axle, and the top is set spinning by applying \( T = 2.90 \, \text{N} \) of constant tension to each string. If it takes \( 0.770 \, \text{s} \) for the string to unwind, how much angular momentum \( L \) does the top acquire? Assume that the strings do not slip as the tension is applied.
**Angular Momentum Equation**
\[ L = \ \, \text{kg} \cdot \text{m}^2/\text{s} \]
(Incorrect answer provided in the problem)
The goal is to determine the angular momentum \( L \) acquired by the top, assuming the strings apply the tension without slipping during the unwinding process.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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![**Diagram Explanation**
This educational diagram depicts a child's top set up on a frictionless surface. The diagram labels several parts of the top and illustrates the forces acting upon it:
- **Axle**: The top has an axle with a radius of \( r = 2.46 \, \text{mm} \). This is where two strings are wrapped around.
- **Tension Force (T)**: Two arrows labeled \( T \) point outward, indicating the constant tension of \( T = 2.90 \, \text{N} \) applied to each string.
- **Diameter of Axle**: The distance marked \( 2r \) is the diameter of the axle, which is twice the radius.
- **Point P**: Located on the surface of the conical part of the top, representing a point where the radius \( R \) and height \( h \) intersect.
- **Angle \(\theta\)**: Indicates the angle of elevation from the base to Point P.
- **Height (\( h \))**: Represents the vertical distance from the base to the top of the conical part.
**Problem Description**
A child's top is held in place upright on a frictionless surface. The axle has a radius of \( r = 2.46 \, \text{mm} \). Two strings are wrapped around the axle, and the top is set spinning by applying \( T = 2.90 \, \text{N} \) of constant tension to each string. If it takes \( 0.770 \, \text{s} \) for the string to unwind, how much angular momentum \( L \) does the top acquire? Assume that the strings do not slip as the tension is applied.
**Angular Momentum Equation**
\[ L = \ \, \text{kg} \cdot \text{m}^2/\text{s} \]
(Incorrect answer provided in the problem)
The goal is to determine the angular momentum \( L \) acquired by the top, assuming the strings apply the tension without slipping during the unwinding process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02b0d8dd-74c4-474c-82fb-c33b821e5fe0%2F5a853d3b-9dab-4cf4-9e7e-b4a1d1e2593c%2Frfjcdon_processed.png&w=3840&q=75)
