5 Questions
Which of the following is the expression for the third kinematical equation of translational motion?
$v^2 = u^2 + 2as$
What is the expression for the moment of inertia of a thin ring or hollow cylinder about its central axis?
$I = MR^2$
What is the expression for the moment of inertia of a uniform disc or solid cylinder about its central axis?
$I = \frac{1}{2}MR^2$
Which of the following is the expression for the angular momentum of a rotational system?
$L = I\omega$
Which of the following is the expression for the torque acting on a rotational system?
$\tau = \frac{dL}{dt}$
Study Notes
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.
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