Rotation of a Flywheel

Introduction

Flywheel: A spinning disk, rotating counterclockwise.
Starts from rest and rotates an angle of 65 radians in 15 seconds.
Objective: Determine average angular speed, direction of angular speed, and tangential speed at different points.

Initial Conditions:
- Starts from rest (initial angular speed = 0).
- Rotational angle = 65 radians.
- Time taken = 15 seconds.
Formula: Average angular speed = Change in angle / Change in time.
- Analogous to average linear speed: Change in distance / Change in time.
- Here, distance is equivalent to rotational angle (theta).
Calculation:
- Final angle = 65 radians, Initial angle = 0.
- Final time = 15 seconds, Initial time = 0.
- Average angular speed = 65 radians / 15 seconds = 4.33 radians/sec.

Right-Hand Thumb/Curl Rule:
- Curl fingers in direction of rotation.
- Thumb points in direction of angular velocity.
Result:
- For counterclockwise rotation, thumb points upwards, indicating angular speed is vertically upward.

Definitions:
- Tangential speed: Speed at a specific location, direction is tangent to the point.
- Formula: Tangential speed = Radius x Angular speed (v = r * ω).
Characteristics:
- Angular speed (ω) is constant across all points of the flywheel.
- Tangential speed varies with radius; greater radius = greater tangential speed.
Example Calculations:
- At 5 cm from the center (converted to meters), tangential speed = (0.05 m) x (4.33 rad/sec) = 0.2165 m/sec.
- Larger radius will yield a higher tangential speed.
Key Points:
- Angular velocity is not dependent on position.
- Tangential speed is position-dependent, increasing with radius.*

Summary: Explained rotation dynamics of a flywheel including average angular speed, direction of angular velocity, and position-dependent tangential speed.
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