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0. Math Review31m
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

12. Rotational Kinematics

Rotational Position & Displacement

Physics

12. Rotational Kinematics

Rotational Position & Displacement

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2:48 minutes

Problem 6

Textbook Question

A child rolls a ball on a level floor 3.1 m to another child. If the ball makes 12.0 revolutions, what is its diameter?

Verified step by step guidance

Determine the total distance traveled by the ball, which is given as 3.1 m.

Recall the relationship between the distance traveled by a rolling object and the number of revolutions it makes: \( d = n \cdot C \), where \( d \) is the distance, \( n \) is the number of revolutions, and \( C \) is the circumference of the ball.

The circumference \( C \) of a circle is related to its diameter \( D \) by the formula \( C = \pi D \). Substitute this into the distance formula: \( d = n \cdot \pi D \).

Rearrange the formula to solve for the diameter \( D \): \( D = \frac{d}{n \cdot \pi} \).

Substitute the given values: \( d = 3.1 \; \text{m} \), \( n = 12.0 \), and \( \pi \approx 3.1416 \) into the formula to calculate \( D \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Circumference of a Circle

The circumference of a circle is the distance around it, calculated using the formula C = πd, where d is the diameter. In this problem, knowing the circumference is essential to relate the number of revolutions the ball makes to its diameter.

Revolutions and Distance

One complete revolution of a circular object corresponds to a distance equal to its circumference. Therefore, if the ball makes 12.0 revolutions, the total distance traveled can be expressed as D = number of revolutions × circumference, which is crucial for determining the diameter.

Linear Distance Measurement

Linear distance measurement refers to the straight-line distance between two points. In this scenario, the ball rolls a total distance of 3.1 m, which is the key measurement needed to calculate the diameter of the ball based on the revolutions it completes.

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Multiple Choice

An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through?

BONUS:How many complete revolutions does it make?

A car travels a total of 2,000 m and 1140° around a circular path, starting from 0° . What is the radius of the circular path?

BONUS:How far (in degrees) from 0° does the car end up?

FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?