Analogous Kinematic Equations: Translation and Rotation

Kinematical Equations for Translational and Rotational Motions

• Average velocity (ʋ) is a key concept in translational motion.
• The first kinematical equation for translational motion is v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.
• The second kinematical equation for translational motion is s = ut + (1/2)at², where s is displacement, u is initial velocity, t is time, and a is acceleration.
• The third kinematical equation for translational motion is v² = u² + 2as, where v is final velocity, u is initial velocity, a is acceleration, and s is displacement.

Analogous Equations for Rotational Motion

• Average angular velocity (α) is a key concept in rotational motion.
• The first kinematical equation for rotational motion is α = ω₀ + αt, where α is average angular velocity, ω₀ is initial angular velocity, α is angular acceleration, and t is time.
• The second kinematical equation for rotational motion is θ = ω₀t + (1/2)αt², where θ is angular displacement, ω₀ is initial angular velocity, t is time, and α is angular acceleration.
• The third kinematical equation for rotational motion is ω² = ω₀² + 2αθ, where ω is final angular velocity, ω₀ is initial angular velocity, α is angular acceleration, and θ is angular displacement.

Analogous Quantities between Translational and Rotational Motions

• Linear displacement and angular displacement are analogous quantities.
• Linear velocity and angular velocity are analogous quantities.
• Linear acceleration and angular acceleration are analogous quantities.
• Mass and moment of inertia are analogous quantities.
• Linear momentum and angular momentum are analogous quantities.
• Force and torque are analogous quantities.
• Work and work done in rotational motion are analogous quantities.
• Power and power in rotational motion are analogous quantities.

Moment of Inertia for Different Objects

• The formula for the moment of inertia of a thin ring or hollow cylinder about its central axis is I = MR², where M is mass and R is radius.
• The formula for the moment of inertia of a thin ring about its diameter is I = (1/4)MR², where M is mass and R is radius.
• The formula for the moment of inertia of an annular ring or thick-walled hollow cylinder about its central axis is I = M((R₁² + R₂²)/2), where M is mass, R₁ is inner radius, and R₂ is outer radius.
• The formula for the moment of inertia of a uniform disc or solid cylinder about its central axis is I = (1/2)MR², where M is mass and R is radius.
• The formula for the moment of inertia of a uniform disc or solid cylinder about its diameter is I = (1/4)MR², where M is mass and R is radius.

Test your knowledge on analogous kinematic equations for translational and rotational motion. The quiz covers equations for average velocity, distance, acceleration, angular velocity, and more.