What is Rotational Motion?
Rotational motion describes how objects turn or spin around a fixed axis, from a spinning wheel to a planet's rotation. It extends the concepts of linear motion — position, velocity, and force — into angular equivalents like angle, angular velocity, and torque.
Rotational motion is the motion of an object around an axis, described by angular displacement (θ), angular velocity (ω = Δθ/Δt), and angular acceleration (α = Δω/Δt), with torque τ = Iα driving changes in spin, just as force drives changes in linear motion.
- •Position x (m)
- •Velocity v = dx/dt (m/s)
- •Acceleration a = dv/dt (m/s²)
- •Mass m (kg)
- •Force F = ma (N)
- •Angle θ (rad)
- •Angular velocity ω = dθ/dt (rad/s)
- •Angular acceleration α = dω/dt (rad/s²)
- •Moment of inertia I (kg·m²)
- •Torque τ = Iα (N·m)
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Step-by-step worked examples
A wheel starts from rest and reaches an angular velocity of 20 rad/s in 4 s. Find its angular acceleration.
α = Δω/Δt = 20/4 = 5 rad/s²
A torque of 12 N·m is applied to a disk with moment of inertia 3 kg·m². Find the angular acceleration.
α = τ/I = 12/3 = 4 rad/s²
A rotor with moment of inertia 2 kg·m² needs an angular acceleration of 6 rad/s². Find the required torque.
τ = Iα = 2 × 6 = 12 N·m
Flashcards
Quick quiz
Q1.Which quantity is the rotational analog of force?
Q2.A disk has moment of inertia 4 kg·m² and angular acceleration 3 rad/s². What is the torque?
Q3.What is the unit of angular acceleration?
Q4.What determines an object's moment of inertia?
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Common mistakes
Thinking mass alone determines moment of inertia. — Correct: The distribution of mass relative to the axis matters (I = Σmr²), not just total mass.
Confusing angular velocity ω with linear velocity v. — Correct: v = ωr relates them, but they are not identical, especially at different radii.
Assuming torque and force are the same thing. — Correct: Torque equals force times lever arm (τ = rF sinθ); it depends on where and how the force is applied.
Ignoring the axis of rotation. — Correct: Moment of inertia and angular quantities all depend on the chosen axis.
FAQ
What is rotational motion?
Rotational motion is motion in which an object turns around an axis, described by angular displacement, angular velocity, and angular acceleration.
What is the formula for rotational motion?
Torque, the driver of rotational motion, is τ = Iα — analogous to F = ma in linear motion.
What are examples of rotational motion?
A spinning wheel, a rotating fan blade, Earth spinning on its axis, and a figure skater's spin.
How do you calculate torque in rotational motion?
Multiply the moment of inertia I by the angular acceleration α: τ = Iα.