A child's top is held in place upright on a frictionless surface. The axle has a radius of \( r = 3.21 \, \text{mm} \). Two strings are wrapped around the axle, and the top is set spinning by applying \( T = 2.40 \, \text{N} \) of constant tension to each string. If it takes \( 0.590 \, \text{s} \) 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. \[ L = 9.15 \times 10^{-3} \, \frac{\text{kg} \cdot \text{m}^2}{\text{s}} \]Point P is located on the outer surface of the top, a distance \( h = 35.0 \, \text{mm} \) above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is \( \theta = 24.0^\circ \). If the final tangential speed \( v_t \) of point P is \( 1.45 \, \text{m/s} \), what is the top's moment of inertia \( I \)?\[ I = 2.42 \times 10^{-4} \, \text{kg} \cdot \text{m}^2 \](Incorrect)### Diagram ExplanationThe first diagram is a side view of the top. It shows:- Two arrows labeled \( T \) representing the tension force applied to the strings, pointing outward.- The radius of the axle (\( 2r \)) and its alignment with the tension arrows.- A point P located on the outer surface at height \( h \).- The angle \( \theta \) illustrating the angle between the surface and the axis.The second diagram is a top view:- It illustrates the axle with the tension forces \( T \) acting in opposite directions across the axle’s diameter (\( 2r \)).These diagrams help in understanding how the forces and dimensions relate to the spinning motion and calculation of angular momentum and moment of inertia.

The radius of the axle is r = 3.21 mm = 3.21 x 10-3 m. The tension applied to each string is T =…

A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. SP h kg-m? L = 9.15 x10-3 S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T T -4 2.42 x10 I = kg-m? Incorrect

A child's top is held in place upright on a frictionless surface. The axle has a radius of r = 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. SP h kg-m? L = 9.15 x10-3 S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T T -4 2.42 x10 I = kg-m? Incorrect

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

A child's top is held in place upright on a frictionless surface. The axle has a radius of \( r = 3.21 \, \text{mm} \). Two strings are wrapped around the axle, and the top is set spinning by applying \( T = 2.40 \, \text{N} \) of constant tension to each string. If it takes \( 0.590 \, \text{s} \) 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.

\[ L = 9.15 \times 10^{-3} \, \frac{\text{kg} \cdot \text{m}^2}{\text{s}} \]

Point P is located on the outer surface of the top, a distance \( h = 35.0 \, \text{mm} \) above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is \( \theta = 24.0^\circ \). If the final tangential speed \( v_t \) of point P is \( 1.45 \, \text{m/s} \), what is the top's moment of inertia \( I \)?

\[ I = 2.42 \times 10^{-4} \, \text{kg} \cdot \text{m}^2 \]

(Incorrect)

### Diagram Explanation

The first diagram is a side view of the top. It shows:
- Two arrows labeled \( T \) representing the tension force applied to the strings, pointing outward.
- The radius of the axle (\( 2r \)) and its alignment with the tension arrows.
- A point P located on the outer surface at height \( h \).
- The angle \( \theta \) illustrating the angle between the surface and the axis.

The second diagram is a top view:
- It illustrates the axle with the tension forces \( T \) acting in opposite directions across the axle’s diameter (\( 2r \)).

These diagrams help in understanding how the forces and dimensions relate to the spinning motion and calculation of angular momentum and moment of inertia.

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