5.1 Rotational Kinematics

• Rotational kinematics studies the motion of objects rotating around a fixed axis
• Angular displacement is measured in radians
• Angular velocity is analogous to linear velocity
• Angular velocity is the rate of change of angular position
• The relationship between linear and angular acceleration is a = rα
• The angular velocity equation for constant angular acceleration is ω = ω₀ + αt
• What is the equation for angular displacement (Δθ)?

  $\Delta\theta =$$\omega_{0} t +$$\frac{1}{2}\alpha t^{2}$
• ω₀ represents the initial angular velocity.


  True
• Rotational kinematics problems can be solved using the relationships between angular quantities.


  True
• Angular quantities are analogous to linear quantities in translational motion.
• What is the relationship between linear displacement (Δx) and angular displacement (Δθ)?

  $\Delta x =$$r \times \Delta\theta$
• Angular acceleration (α) is the rate of change of angular velocity.
• What is the equation for final angular velocity (ω) with constant angular acceleration?

  \omega = \omega_{0} + \alpha t</latex>
• What is the formula for final angular velocity (ω) with constant angular acceleration?

  $\omega =$$\omega_{0} +$$\alpha t$
• Match the quantity with its equation:

  Angular displacement (Δθ) ↔️ $\Delta\theta =$$\omega_{0} t +$$\frac{1}{2}\alpha t^{2}$

  Angular velocity (ω) ↔️ $\omega =$$\omega_{0} +$$\alpha t$

  Angular acceleration (α) ↔️ Constant
• A wheel with a radius of 0.5 m accelerates at 4 rad/s² for 3 seconds. Its final angular velocity is 12 rad/s.


  True
• What is the final angular velocity of a wheel that starts from rest and accelerates uniformly at 2 rad/s² for 5 seconds?

  10 rad/s
• What is the linear displacement of a point on the rim of a wheel with radius 0.5 m that rotates through an angle of 2π rad?

  3.14 m
• What is the linear speed of a point on the edge of a turntable with a radius of 0.3 m that rotates at 2 rad/s?

  0.6 m/s
• What is the unit of angular acceleration?

  rad/s²
• The angular displacement equation for constant angular acceleration is Δθ = ω₀t + ½αt²


  True
• The unit of angular velocity (ω) is rad/s
• In the equation $\Delta\theta =$$\omega_{0} t +$$\frac{1}{2}\alpha t^{2}$, 't' represents time
• Match the angular quantity with its unit:

  Angular position ↔️ radians

  Angular velocity ↔️ rad/s

  Angular acceleration ↔️ rad/s²
• Angular displacement is measured in radians.

  True
• When an object rotates with constant angular acceleration, its angular velocity changes uniformly.

  True
• The formula for angular displacement (Δθ) with constant angular acceleration is \Delta\theta = \omega_{0} t + \frac{1}{2}\alpha t^{2}
• What is the relationship between linear displacement (Δx) and angular displacement (Δθ)?

  $\Delta x =$$r \Delta \theta$
• A car tire with a radius of 0.3 m travels 5 m. What is the angular displacement?

  16.67 rad
• Steps to apply rotational kinematic equations

  1️⃣ Identify the given quantities

  2️⃣ Choose the appropriate equation

  3️⃣ Substitute the values

  4️⃣ Solve for the unknown
• The constant angular acceleration (α) is measured in units of rad/s²
• Angular velocity is measured in rad/s


  True
• The relationship between angular and linear displacement is Δθ = Δx/r


  True
• The relationship between linear and angular velocity is v = rω

  True
• Angular velocity is the rate of change of angular position


  True
• What is the linear acceleration of a point on the rim of a wheel (r = 0.3 m) that accelerates uniformly at 2 rad/s² for 5 seconds?

  0.6 m/s²
• What does ω₀ represent in rotational kinematics equations?

  Initial angular velocity
• What does Δθ represent in rotational kinematics?

  Change in angular position
• What is the unit of angular acceleration (α)?

  rad/s²
• What does rotational kinematics study?

  Motion around a fixed axis