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

12. Rotational Kinematics

Equations of Rotational Motion

Physics

12. Rotational Kinematics

Equations of Rotational Motion

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Multiple Choice

The turntable of a DJ set is spinning at a constant rate just before it is turned off. If the turntable decelerates at 3 rad/s² and goes through an additional 30 rotations before stopping, how fast (in RPM) was the turntable initially spinning?
BONUS:How long (in seconds) does the turntable take to stop?

33.6 RPM

321 RPM

2,016 RPM

3,167 RPM

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Verified step by step guidance

First, convert the number of rotations into radians. Since one rotation is equal to 2π radians, multiply 30 rotations by 2π to get the total angular displacement in radians.

Use the kinematic equation for rotational motion: θ = ω₀t + 0.5αt², where θ is the angular displacement, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time. Since the turntable stops, the final angular velocity ω is 0.

Rearrange the kinematic equation to solve for the initial angular velocity ω₀: ω₀² = ω² + 2αθ. Substitute ω = 0, α = -3 rad/s² (deceleration), and θ from step 1.

Calculate ω₀ in rad/s using the values from the previous step. Then, convert ω₀ from rad/s to RPM (revolutions per minute) using the conversion factor: 1 rad/s = 60/(2π) RPM.

For the bonus question, use the equation ω = ω₀ + αt to solve for the time t it takes for the turntable to stop. Substitute ω = 0, ω₀ from step 4, and α = -3 rad/s².