5.1 Rotational Kinematics

• Rotational Motion is the movement of an object around an axis
• What unit is used to measure angular displacement?

  Radians
• Linear displacement measures the change in angle during rotation.

  False
• Angular Acceleration is the rate of change of angular velocity over time.
• What is the formula for angular acceleration?

  $\alpha =$$\frac{\Delta \omega}{\Delta t}$
• Linear displacement corresponds to angular displacement in rotational motion.


  True
• The rotational kinematic equations allow us to solve problems involving objects undergoing rotational motion.
• What is angular velocity defined as?

  Rate of change of angular displacement
• The formula for angular velocity is \(\omega = \frac{\Delta \theta}{\Delta t}\)
• The formula for angular acceleration is \(\alpha = \frac{\Delta \omega}{\Delta t}\)
• Another rotational kinematic equation is \(\omega = \omega_i + \alpha t\)
• Steps to solve rotational motion problems using kinematic equations

  1️⃣ Identify the known values

  2️⃣ Determine which rotational kinematic equation is appropriate

  3️⃣ Plug in the known values

  4️⃣ Solve for the unknown quantity
• What are the three rotational kinematic variables used in the rotational kinematic equations?

  Angular displacement, velocity, acceleration
• The rotational equivalent of the linear kinematic equation \(\Delta x = v_i t + \frac{1}{2}at^2\) is \(\Delta \theta\)
• The equation \(\omega^2 = \omega_i^2 + 2\alpha\Delta \theta\) relates final angular velocity to initial angular velocity, angular acceleration, and angular displacement.

  True
• Steps to solve a problem using rotational kinematic equations

  1️⃣ Identify the known values

  2️⃣ Determine the appropriate equation

  3️⃣ Plug in the known values

  4️⃣ Solve for the unknown quantity
• What is the unit of measurement for angular displacement?

  radians
• Rotational motion involves movement around an axis along a circular path.


  True
• Angular velocity is the rate of change of angular displacement
• What is the formula for angular acceleration?

  \(\alpha = \frac{\Delta \omega}{\Delta t}\)
• What is the formula for angular velocity (\(\omega\))?

  $\omega =$$\frac{\Delta \theta}{\Delta t}$
• Angular acceleration (\(\alpha\)) is the rate of change of angular
• Angular velocity (\(\omega\)) is the rate of change of angular displacement (\(\Delta \theta\)) over time
• What do the rotational kinematic equations relate?

  \(\Delta \theta, \omega, \alpha\)
• The rotational kinematic equation for angular displacement is $\Delta \theta =$$\omega_{i} t +$$\frac{1}{2}\alpha t^{2}$


  True
• The rotational kinematic equation for angular velocity is $\omega =$$\omega_{i} +$$\alpha t$, which is equivalent to its linear counterpart velocity
• In the example problem, what are the known values?

  \(\omega_i = 0\) rad/s, \(\alpha = 5\) rad/s², \(t = 4\) s
• Rotational kinematic problems are solved using angular quantities and rotational kinematic equations.

  True
• Match the unit with its corresponding variable in rotational kinematics:

  radian ↔️ \(\Delta \theta\)

  rad/s ↔️ \(\omega\)

  rad/s² ↔️ \(\alpha\)
• The angular acceleration in Example 1 is negative.

  False
• What is the final angular velocity of the spinning top in Example 2?

  0 rad/s
• The angular deceleration in Example 2 is -5 rad/s^2.
• The equation $\omega =$$\omega_{i} +$$\alpha t$ relates initial and final angular velocities with time and angular acceleration.


  True
• How long does it take for the spinning top in Example 2 to come to rest?

  4 seconds
• Match the variables with their units in rotational kinematics:

  Angular velocity ↔️ rad/s

  Angular acceleration ↔️ rad/s^2

  Angular displacement ↔️ rad

  Time ↔️ s
• What is the initial angular velocity of the wheel in Example 1?

  10 rad/s
• The equation $\Delta \theta =$$\omega_{i} t +$$\frac{1}{2}\alpha t^{2}$ can be used for constant angular velocity.


  True
• What is the angular displacement of the wheel in Example 1 after 5 seconds?

  112.5 rad
• The equation \omega = \omega_i + \alpha t</latex> is used to find the final angular velocity.
• Angular displacement is calculated as \(\Delta \theta = \theta_f - \theta_i\), where \(\theta_f\) is the final angle and \(\theta_i\) is the initial