5.1 Rotational Kinematics

• What is angular displacement measured in?

  Radians
• Angular displacement is represented by the Greek letter theta
• Angular displacement describes rotation around a fixed axis, while linear displacement describes straight-line motion.
• What is angular velocity measured in?

  Rad/s
• Angular velocity is represented by the Greek letter omega
• Angular acceleration is the rate of change of angular velocity over time.
• What is angular acceleration measured in?

  Rad/s²
• Angular acceleration is represented by the Greek letter alpha
• The kinematic equations for rotational motion are analogous to linear motion equations.
• Match the rotational kinematic equation with its description:

  ω = ω₀ + αt ↔️ Final angular velocity

  θ = ω₀t + ½αt² ↔️ Angular displacement

  ω² = ω₀² + 2αθ ↔️ Velocity-displacement relationship
• Arrange the steps to solve a rotational motion problem:

  1️⃣ Identify known variables

  2️⃣ Select appropriate equation

  3️⃣ Substitute values into equation

  4️⃣ Solve for unknown variable
• What is the relationship between linear velocity and angular velocity?

  v = rω
• Linear acceleration is equal to the radius times the angular acceleration
• Angular displacement is the change in the angular position of an object measured in radians.
• Match the property with its description:

  Angular Displacement ↔️ Change in angular position

  Angular Velocity ↔️ Rate of change of angular displacement

  Angular Acceleration ↔️ Rate of change of angular velocity
• Angular displacement is defined as the change in angular position.
• The unit of angular displacement is radians.
• Angular displacement describes the rotation of an object around a fixed axis
• Linear displacement describes straight-line motion.
• Angular velocity is measured in radians per second
• Angular acceleration is the rate of change of angular velocity over time.
• Match the property with its corresponding unit:

  Angular velocity ↔️ rad/s

  Linear velocity ↔️ m/s

  Angular acceleration ↔️ rad/s²

  Linear acceleration ↔️ m/s²
• The formula for angular velocity is ω = Δθ / Δt
• The formula for angular acceleration is α = Δω / Δt.
• The rotational kinematic equation for final angular velocity is ω = ω₀ + αt
• The angular displacement equation is θ = ω₀t + ½αt².
• The velocity-displacement relationship for rotational motion is ω² = ω₀² + 2αθ
• Linear velocity is related to angular velocity by the formula v = rω.
• Linear acceleration is related to angular acceleration by the formula a = rα
• The linear velocity of a point on a rotating object is equal to the radius of rotation times the angular velocity.
• The choice of which rotational kinematic equation to use depends on the unknown variable
• Steps to solve rotational motion problems:

  1️⃣ Identify the given information

  2️⃣ Determine which rotational kinematic equation to use

  3️⃣ Plug in the known values and solve for the unknown

  4️⃣ Use the radius of rotation to find linear quantities if needed
• Linear and angular quantities are related by the radius of rotation