Rotational Kinematics & Angular Momentum
Interactive 3D rotational mechanics simulator. Drop point masses onto a spinning disk to observe angular momentum conservation and kinetic energy dissipation.
ROTATIONAL VARIABLES
Rotational kinematics is the study of rotating objects using variables analogous to linear kinematics. 1. **Angular Position ()** in radians (analogous to ). 2. **Angular Velocity ()** in rad/s (analogous to ). 3. **Angular Acceleration ()** in rad/s² (analogous to ). These variables are connected to linear motion through the radius : , , and .
ROTATIONAL KINEMATIC EQUATIONS
For constant angular acceleration, we use a set of equations identical in form to the "Big Four" linear equations. For example, mirrors . All AP Physics 1 concepts like displacement, velocity, and acceleration have their counterparts in the rotational world. Remember: **always use radians** for rotational kinematics calculations!
HOW TO USE THIS VISUALIZATION
1. **Spin the Wheel**: Adjust the constant angular acceleration and watch the wheel speed up. 2. **Track a Point**: Observe a point on the rim. Watch its linear velocity () and tangential acceleration () change while the angular values remain consistent for all points. 3. **Compare Graphs**: Look at the -, -, and - graphs and notice their similarity to the 1D linear motion graphs.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 5: Torque and Rotational Dynamics (Topic 5.1)
Learning Objective: 2.1.1
COMMON MISCONCEPTIONS
- Confusing angular velocity (rad/s) with tangential velocity (m/s).
- Forgetting to use radians (360° = radians).
- Mixing linear and rotational variables in the same equation without the factor of .
KEY TAKEAWAYS
- Angular variables are related to linear ones via .
- Rigid bodies have a single and for all points.
- Rotational equations mirror linear equations.
- Angular acceleration requires a net torque.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): A wheel accelerates from rest at 2 rad/s² for 4 seconds. What is its final angular velocity?
Show Answer & Explanation
Answer: 8 rad/s
Explanation: rad/s.
Q2 (CONCEPTUAL): Two points on a rotating disk are at different distances from the center. Which has a larger angular velocity?
Show Answer & Explanation
Answer: They have the same angular velocity.
Explanation: All points on a rigid rotating object have the same angular velocity () because they sweep through the same angle in the same time.
DEEP DIVE: RELATED CONCEPTS
Torque (\tau) is the rotational equivalent of force. It is a measure of how much a force acting on a...
WHAT IS ANGULAR MOMENTUM?Angular momentum ($L$) is the measure of an object's rotational motion. Just as linear momentum ($p ...
UNDERSTANDING CENTRIPETAL FORCECentripetal force is not a separate "new" force; it is the **net force** that points toward the cent...
