A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 4.21 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 1.65 N of constant tension to each string. If it %3D takes 0.740 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. L = kg-m2 Point P is located on the outer surface of the top, a distance h = 31.0 mm above the ground. The angle that the outer %3D surface of the top makes with the rotation axis of the top is 0 = 28.0°. If the final tangential speed v of point P is 1.05 m/s, what is the top's moment of inertia I?
A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 4.21 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 1.65 N of constant tension to each string. If it %3D takes 0.740 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. L = kg-m2 Point P is located on the outer surface of the top, a distance h = 31.0 mm above the ground. The angle that the outer %3D surface of the top makes with the rotation axis of the top is 0 = 28.0°. If the final tangential speed v of point P is 1.05 m/s, what is the top's moment of inertia I?
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![**Text Transcription for Educational Website**
A child's top is held in place upright on a frictionless surface. The axle has a radius of \( r = 4.21 \, \text{mm} \). Two strings are wrapped around the axle, and the top is set spinning by applying \( T = 1.65 \, \text{N} \) of constant tension to each string. If it takes \( 0.740 \, \text{s} \) 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.
\[ L = \quad \fbox{\makebox[2cm]{}} \quad \text{kg} \cdot \text{m}^2/\text{s} \]
Point P is located on the outer surface of the top, a distance \( h = 31.0 \, \text{mm} \) above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is \( \theta = 28.0^\circ \). If the final tangential speed \( v_t \) of point P is \( 1.05 \, \text{m/s} \), what is the top's moment of inertia \( I \)?
\[ I = \quad \fbox{\makebox[2cm]{}} \quad \text{kg} \cdot \text{m}^2 \]
**Explanation of Diagrams**
- **Top Diagram**: This diagram shows a side view of the child's top. The top has a conical shape. The axle at the top, with strings wrapped around it, is experiencing a tension \( T \) applied in opposite directions. This tension causes the top to rotate. The radius of the axle is \( 2r \), and point P is marked on the conical surface, with distance \( h \) from the ground and angle \( \theta \) to the rotation axis.
- **Bottom Diagram**: This shows a top-down view of the axle, detailing the two strings exerting tension \( T \) in opposite directions. This tension facilitates the rotational motion by unwinding the strings around the axle (radius \( 2r \)).
These diagrams illustrate the physical setup needed to understand and solve the problems of angular momentum and moment of inertia for the spinning top.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf6d6073-84a9-46c5-8488-6d3f77fb711e%2F1758a97c-2e2e-4cc2-8d5c-be1c05662b01%2F3ord70h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text Transcription for Educational Website**
A child's top is held in place upright on a frictionless surface. The axle has a radius of \( r = 4.21 \, \text{mm} \). Two strings are wrapped around the axle, and the top is set spinning by applying \( T = 1.65 \, \text{N} \) of constant tension to each string. If it takes \( 0.740 \, \text{s} \) 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.
\[ L = \quad \fbox{\makebox[2cm]{}} \quad \text{kg} \cdot \text{m}^2/\text{s} \]
Point P is located on the outer surface of the top, a distance \( h = 31.0 \, \text{mm} \) above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is \( \theta = 28.0^\circ \). If the final tangential speed \( v_t \) of point P is \( 1.05 \, \text{m/s} \), what is the top's moment of inertia \( I \)?
\[ I = \quad \fbox{\makebox[2cm]{}} \quad \text{kg} \cdot \text{m}^2 \]
**Explanation of Diagrams**
- **Top Diagram**: This diagram shows a side view of the child's top. The top has a conical shape. The axle at the top, with strings wrapped around it, is experiencing a tension \( T \) applied in opposite directions. This tension causes the top to rotate. The radius of the axle is \( 2r \), and point P is marked on the conical surface, with distance \( h \) from the ground and angle \( \theta \) to the rotation axis.
- **Bottom Diagram**: This shows a top-down view of the axle, detailing the two strings exerting tension \( T \) in opposite directions. This tension facilitates the rotational motion by unwinding the strings around the axle (radius \( 2r \)).
These diagrams illustrate the physical setup needed to understand and solve the problems of angular momentum and moment of inertia for the spinning top.
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