Rotational Dynamics and Circular Motion Vocabulary

Flashcards on Rotational Dynamics and Circular Motion based on lecture notes.

Circular Motion

Motion where an object or particle moves along a circular path or trajectory.

Uniform Circular Motion (UCM)

Circular motion where the speed of the particle remains constant, and the direction of velocity changes continuously.

Centripetal Acceleration

Acceleration directed towards the center of the circular motion, responsible for changing the direction of the velocity in UCM.

Non-uniform Circular Motion

Circular motion where the speed of the particle changes over time.

Tangential Acceleration

Acceleration directed along the tangent to the circular path, responsible for changing the magnitude of the velocity in non-uniform circular motion.

Centripetal Force

The resultant force acting on a body undergoing circular motion, directed towards the center of the circle.

Centrifugal Force

A pseudo force that appears to act outward on a rotating object, experienced in the non-inertial frame of reference of the rotating object.

Banking of Roads

The practice of tilting the surfaces of curved roads with respect to the horizontal to provide centripetal force.

Conical Pendulum

A system consisting of a point mass (bob) connected to a string revolving in a horizontal circle, with the string tracing a cone.

Moment of Inertia (I)

The measure of an object's resistance to rotational acceleration about a given axis; analogous to mass in linear motion.

Radius of Gyration (K)

The distance from the axis of rotation at which the entire mass of an object can be assumed to be concentrated without changing its moment of inertia.

Theorem of Parallel Axes

The moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis through the center of mass and the product of the mass of the body and the square of the distance between the axes.

Theorem of Perpendicular Axes

For a laminar object, the moment of inertia about an axis perpendicular to the plane of the object is equal to the sum of the moments of inertia about two perpendicular axes in the plane of the object that intersect at the same point.

Angular Momentum

The rotational equivalent of linear momentum; a measure of the amount of rotational motion an object has.

Torque (\tau)

A twisting force that causes rotation; the product of the force and the lever arm.

Rotational Kinetic Energy

The kinetic energy due to the rotation of an object and is proportional to the moment of inertia and the square of the angular velocity. KE_{rot} = \frac{1}{2}I\omega^2

Work Done in Rotation

The work done by a torque in rotating an object through an angle. W = \tau \theta

Power in Rotational Motion

The rate at which work is done in rotational motion. P = \tau \omega

Angular Impulse

The change in angular momentum of an object. It’s the rotational equivalent of linear impulse.

Conservation of Angular Momentum

In the absence of external torques, the total angular momentum of a rotating system remains constant.

Rolling Motion

A combination of translational and rotational motion, such as a wheel rolling along a surface.

Kinetic Energy in Rolling Motion

The sum of translational and rotational kinetic energies for an object undergoing rolling motion. KE = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2

Instantaneous Axis of Rotation

The axis about which a rigid body appears to be rotating at a particular instant during rolling motion.

Simple Harmonic Motion (SHM)

A type of periodic motion where the restoring force is directly proportional to the displacement, causing oscillation about an equilibrium position.

Amplitude (A)

The maximum displacement from the equilibrium position in SHM.

Period (T)

The time taken for one complete oscillation in SHM.

Frequency (f)

The number of oscillations per unit time in SHM, which is the reciprocal of the period. f = \frac{1}{T}

Angular Frequency ($\omega$)

Related to the frequency and period by \omega = 2\pi f = \frac{2\pi}{T}, representing the rate of change of the angle of oscillation.

Phase Constant ($\phi$)

Determines the initial position of the oscillating object at time t = 0 in SHM.