Rotational Kinematics

Importance of Key Equations

• The second and third equations of motion are crucial in solving problems.

• The last equation focuses on finding average velocity; however, it is not emphasized as much as the first three equations.

• Emphasis is placed on understanding and applying the first three equations in various contexts.

Angular Version of Equations

• Exchange linear terms for angular terms to derive angular formulas.

• The process involves substituting keywords:

  • Displacement (d) becomes Angular Displacement (θ)

  • Time (t), Final Velocity (v), and Acceleration (a) change to Angular Velocity (ω), and Angular Acceleration (α) respectively.

• Understanding this conversion is key for future problems, particularly for numbers 1-19.

Sample Problem: Tricycle Wheel

• Problem Statement: A tricycle wheel of radius 0.55 m accelerates at 1.2 rad/s² for 10.5 seconds. Find the wheel's final angular and linear velocity.

• Equations Used:

  • Angular Velocity: ( ω = ω_0 + αt )

  • Linear Velocity: ( v = rω )

• Calculations:

  1. Apply the equation for angular velocity:

     • Here, initial angular velocity (ω0) = 0, α = 1.2 rad/s², and t = 10.5 s.

     • Calculation: ( ω = 0 + (1.2)(10.5) \approx 12.6 ) rad/s

  2. Find Linear Velocity:

     • Calculation: ( v = 0.55 imes 12.6 \approx 6.9 ) m/s

• Emphasizes the straightforwardness of these calculations.

Practice Questions

• Students are encouraged to attempt additional problems, such as finding angular displacement.

• Given equation for displacement: ( θ = ω_0 t + \frac{1}{2}αt^2 )

• Expected Outcome: Example value for angular displacement = 44.2 (units not specified).

Upcoming Assessment

• An evaluation in the form of a quiz or test on rotational kinematics will be held, focuses on understanding key concepts covered in class.

• Coordination of details regarding the test date is ongoing, but it is expected to take place on Monday, subject to confirmation during class review.

• Students should come prepared and ready to practice before the assessment.