5.1 Rotational Kinematics

• Angular velocity is defined as the change in angular displacement divided by the change in time
• What is the unit of angular acceleration?

  rad/s^2
• The direction of angular velocity is perpendicular to the plane of rotation


  True
• What is the angular equivalent of linear displacement?

  Angular displacement
• The formula relating linear and angular displacement is x = r θ
• What is the key formula to convert linear displacement to angular displacement?

  $x =$$rθ$
• The formulas for converting linear and angular quantities relate the motion of an object rotating around a fixed axis.


  True
• What is the formula for angular displacement in terms of initial angular velocity, time, and angular acceleration?

  θ = ω₀t + 1/2 αt²</latex>
• What is the formula for angular acceleration in terms of initial and final angular velocities and time?

  α = (ω - ω₀) / t</latex>
• Match the rotational kinematic quantity with its symbol and unit:

  Angular Displacement ↔️ θ (radians)

  Initial Angular Velocity ↔️ ω₀ (rad/s)

  Angular Acceleration ↔️ α (rad/s²)
• What does the variable 'α' represent in the kinematic equations for rotational motion?

  Angular acceleration
• What is the unit of angular displacement?

  Radians
• What is the formula for angular velocity?

  $ω =$$Δθ / Δt$
• Angular velocity is a vector quantity with both magnitude and direction.


  True
• Angular acceleration is measured in radians per second squared
• Match the linear quantity with its angular counterpart:

  Linear Displacement ↔️ Angular Displacement

  Linear Velocity ↔️ Angular Velocity

  Linear Acceleration ↔️ Angular Acceleration
• The formula to convert linear displacement to angular displacement is x = rθ.


  True
• What is the formula for angular displacement in rotational kinematics?

  $θ =$$ω₀t +$$1 / 2 αt²$
• What is the formula for angular acceleration in rotational kinematics?

  α = (ω - ω₀) / t</latex>
• The variable ω in rotational kinematics represents the final angular velocity.


  True
• Steps to solve rotational kinematics problems

  1️⃣ Identify given variables

  2️⃣ Choose the appropriate equation

  3️⃣ Solve for the unknown variable
• The radius of rotation is represented by the variable r
• ω₀ represents the initial angular velocity in rotational kinematics.


  True
• The formula to convert linear displacement to angular displacement is x = rθ
• Suppose a wheel with a radius of 0.5 m starts from rest and undergoes a constant angular acceleration of 2 rad/s². What is the angular displacement after 3 seconds?

  $9 \, \text{rad}$
• What is the formula for final angular velocity in terms of initial angular velocity, angular acceleration, and time?

  $\omega =$$\omega_{0} +$$\alpha t$
• A wheel with a radius of 0.5 m starts from rest and undergoes a constant angular acceleration of 2 rad/s². What is the linear velocity of a point on the rim after 3 seconds?

  $3 \, \text{m / s}$
• The formula to convert linear velocity to angular velocity is v = rω
• What is the formula for calculating linear acceleration from angular acceleration and radius?

  $a =$$r \alpha$
• The relationship between linear displacement and angular displacement is given by x = rθ.


  True
• Suppose a wheel with a radius of 0.5 m starts from rest and undergoes a constant angular acceleration of 2 rad/s². What is its final angular velocity after 3 seconds?

  $6 \, \text{rad / s}$
• The linear velocity of a point on the rim of a rotating wheel is constant if the angular velocity is constant.


  True
• A wheel with a radius of 0.5 m starts from rest and undergoes a constant angular acceleration of 2 rad/s². What is its angular displacement after 3 seconds?

  $9 \, \text{rad}$
• Suppose a wheel with a radius of 0.5 m starts from rest and undergoes a constant angular acceleration of 2 rad/s². What is its final angular velocity after 3 seconds?

  $6 \, \text{rad / s}$
• The angular displacement of a wheel starting from rest with an angular acceleration of 2 rad/s² after 3 seconds is 9 rad.


  True
• What is angular displacement measured in?

  Radians
• Angular velocity is a vector quantity

  True
• Angular acceleration is the rate of change of angular velocity
• Match the concept with its symbol and unit:

  Angular Displacement ↔️ θ, radians

  Angular Velocity ↔️ ω, rad/s
• The kinematic equations for rotational motion assume constant angular acceleration


  True