Rotational Kinematics

Rotational Kinematics

• Rotational Motion: Motion of an object around a fixed axis.
• Angular Displacement (Δθ): Change in angular position, measured in radians.
• Angular Velocity (ω): Rate of change of angular displacement, measured in rad/s.
• Angular Acceleration (α): Rate of change of angular velocity, measured in rad/s².

Rotational Kinematics Equations

• Angular Displacement: Δθ = θ₂ - θ₁
• Angular Velocity: ω = Δθ / Δt
• Angular Acceleration: α = Δω / Δt
• Rotational Kinematic Equations:
  1. θ = θ₀ + ω₀t + (1/2)αt²
  2. ω = ω₀ + αt
  3. ω² = ω₀² + 2α(Δθ)

Rotational Dynamics

• Torque (τ): Rotational force that causes an object to rotate, measured in Nm.
• Rotational Inertia (I): Measure of an object's resistance to changes in its rotational motion, measured in kgm².
• Rotational Kinetic Energy (K): Energy of an object due to its rotational motion, measured in J.

Rotational Dynamics Equations

• Torque: τ = r x F = rFsin(θ)
• Rotational Kinetic Energy: K = (1/2)Iω²
• Rotational Equilibrium: Στ = 0 (net torque is zero)
• Rotational Motion with Constant Torque: α = τ / I

Moment of Inertia

• Moment of Inertia (I): Depends on the shape and size of the object, and the axis of rotation.
• Parallel Axis Theorem: I = I₀ + md² (where I₀ is the moment of inertia about the axis through the center of mass, m is the mass of the object, and d is the distance from the axis of rotation to the center of mass)

Rotational Kinematics

• Rotational motion occurs around a fixed axis.
• Angular displacement (Δθ) is the change in angular position, measured in radians.
• Angular velocity (ω) is the rate of change of angular displacement, measured in rad/s.
• Angular acceleration (α) is the rate of change of angular velocity, measured in rad/s².

Rotational Kinematics Equations

• Angular displacement equation: Δθ = θ₂ - θ₁
• Angular velocity equation: ω = Δθ / Δt
• Angular acceleration equation: α = Δω / Δt
• Rotational kinematic equations:
  • θ = θ₀ + ω₀t + (1/2)αt²
  • ω = ω₀ + αt
  • ω² = ω₀² + 2α(Δθ)

Rotational Dynamics

• Torque (τ) is a rotational force that causes an object to rotate, measured in Nm.
• Rotational inertia (I) measures an object's resistance to changes in its rotational motion, measured in kgm².
• Rotational kinetic energy (K) is the energy of an object due to its rotational motion, measured in J.

Rotational Dynamics Equations

• Torque equation: τ = r x F = rFsin(θ)
• Rotational kinetic energy equation: K = (1/2)Iω²
• Rotational equilibrium equation: Στ = 0 (net torque is zero)
• Rotational motion with constant torque equation: α = τ / I

Moment of Inertia

• Moment of inertia (I) depends on the shape and size of the object, and the axis of rotation.
• Parallel axis theorem equation: I = I₀ + md² (where I₀ is the moment of inertia about the axis through the center of mass, m is the mass of the object, and d is the distance from the axis of rotation to the center of mass)

Learn about rotational motion, angular displacement, angular velocity, and angular acceleration, including their equations and units.