Table of contents

0. Math Review31m
- Math Review
  31m
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

15. Rotational Equilibrium

Review: Center of Mass

Physics

15. Rotational Equilibrium

Review: Center of Mass

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Multiple Choice

A hammer can be modeled as a $750 g$ point mass on the end of a $42 cm$ long, $200 g$ uniform rod. How far from the head of the hammer is the center of mass?

2.3 cm

3.1 cm

5.6 cm

6.3 cm

4.4 cm

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Verified step by step guidance

First, understand the concept of the center of mass. The center of mass of a system is the point where the total mass of the system can be considered to be concentrated. For a system of particles, it is calculated using the weighted average of their positions.

Identify the masses and their positions. The hammer head is modeled as a point mass of 750 g, and the rod is a uniform mass of 200 g with a length of 42 cm. The center of mass of the rod is at its midpoint, which is 21 cm from the end of the rod.

Set up the equation for the center of mass. The center of mass $ x_{cm} $ can be calculated using the formula: $ x_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2} $, where $ m_1 $ and $ m_2 $ are the masses, and $ x_1 $ and $ x_2 $ are their respective positions.

Substitute the values into the equation. Let the position of the hammer head be at $ x_1 = 0 $ cm (since we are measuring from the head of the hammer), and the position of the center of mass of the rod be $ x_2 = 21 $ cm. The masses are $ m_1 = 750 $ g and $ m_2 = 200 $ g.

Calculate the center of mass using the formula: $ x_{cm} = \frac{750 \, \text{g} \times 0 \, \text{cm} + 200 \, \text{g} \times 21 \, \text{cm}}{750 \, \text{g} + 200 \, \text{g}} $. Simplify the expression to find the distance from the head of the hammer to the center of mass.