Unit 5: Torque and Rotational Dynamics
Objects do not only move from place to place; they also turn. This unit repeats the ideas of Units 1 and 2 for rotation: angles instead of positions, torques instead of forces, rotational inertia instead of mass.
What you will master
- Describe rotation with angular position θ, angular velocity ω and angular acceleration α, and use the constant α equations.
- Connect rotation to the motion of a point on the object: s = r θ, v = r ω, a = r α (tangential).
- Find the torque of a force about an axis: τ = r F sin θ, and tell which way it turns the object.
- Explain rotational inertia: it depends on the mass and how far it is from the axis (I = Σ m r² for small masses).
- Use rotational equilibrium (net torque zero and net force zero) for seesaws, beams and hanging signs.
- Use Newton's second law in rotational form: α = τ_net / I, also for a pulley with hanging masses.
Rule used on every page: choose the axis and the positive turning direction (usually counterclockwise) before writing any torque.
Topics
Do them in order. Each one follows the same path: story, idea, play, worked examples, practice, common mistakes. Then play the games and finish with the practice set.
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How this unit connects
Each rotational quantity has a partner from Units 1 and 2: θ ↔ x, ω ↔ v, α ↔ a, τ ↔ F, I ↔ m. Unit 6 continues with the energy and angular momentum of rotating objects, including rolling.