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

13. Rotational Inertia & Energy

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Multiple Choice

A small 10-kg object is connected to the right end of a thin rod of length 4 m and mass 5 kg. The rod is free to rotate about a fixed perpendicular axis on its left end, as shown below. The rod is initially held at rest, horizontally. When the rod is released, it falls, rotating about its axis, similar to a pendulum. What is the speed at the rod's center of mass when the rod is vertical? BONUS:What is object's speed when the rod is vertical?

4.4 m/s

4.9 m/s

5.6 m/s

6.1 m/s

Next problem

Verified step by step guidance

Identify the system: A rod of mass 5 kg and length 4 m with a 10 kg object attached at the end. The rod rotates about a fixed axis at its left end.

Calculate the moment of inertia (I) of the system. The moment of inertia of the rod about its end is I_rod = (1/3) * m_rod * L^2, and for the point mass at the end, I_mass = m_object * L^2. Add these to get the total moment of inertia: I_total = I_rod + I_mass.

Use conservation of energy. Initially, the potential energy (PE_initial) is due to the height of the center of mass of the rod and the object. When the rod is vertical, all this energy is converted into rotational kinetic energy (KE_rotational). Set PE_initial = KE_rotational.

Express the rotational kinetic energy as KE_rotational = (1/2) * I_total * ω^2, where ω is the angular velocity. Solve for ω using the energy conservation equation.

Find the linear speed of the center of mass of the rod using v_cm = ω * (L/2), where L/2 is the distance from the axis to the center of mass of the rod. For the object's speed, use v_object = ω * L.

16:46m

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