Front

What is the relationship between the speed of a satellite and its orbital radius?

Back

The speed of a satellite in a circular orbit is inversely proportional to the square root of its orbital radius. As the radius increases, the speed decreases.

Front

Define gravitational potential energy (U) in the context of a satellite orbiting Earth.

Back

Gravitational potential energy (U) is the energy an object possesses due to its position in a gravitational field, calculated as U = -G(m1*m2)/r, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between their centers.

Front

What is the principle of conservation of energy in a mechanical system?

Back

The principle of conservation of energy states that the total energy in a closed system remains constant over time. Energy can neither be created nor destroyed, only transformed from one form to another.

Front

Explain the concept of rolling without slipping.

Back

Rolling without slipping occurs when an object rolls on a surface such that the point of contact is momentarily at rest relative to the surface, meaning the linear speed of the center of mass equals the angular speed times the radius.

Front

What is angular momentum and how is it conserved in a system?

Back

Angular momentum (L) is the rotational equivalent of linear momentum, defined as L = Iω, where I is the moment of inertia and ω is the angular velocity. Angular momentum is conserved in a system when no external torques act on it.

Front

Define moment of inertia (I) and its significance in rotational motion.

Back

Moment of inertia (I) is a measure of an object's resistance to changes in its rotational motion, depending on the mass distribution relative to the axis of rotation. It is calculated as I = Σmr^2 for discrete masses.

Front

What is the relationship between kinetic energy and potential energy in a falling object?

Back

As an object falls, its gravitational potential energy decreases while its kinetic energy increases, maintaining the total mechanical energy constant in the absence of air resistance.

Front

Explain the concept of torque and its role in rotational dynamics.

Back

Torque (τ) is a measure of the rotational force applied to an object, calculated as τ = rFsin(θ), where r is the distance from the pivot point to the point of force application, F is the force, and θ is the angle between the force and the lever arm.

Front

What is the difference between translational and rotational kinetic energy?

Back

Translational kinetic energy (KE) is the energy due to linear motion, given by KE = (1/2)mv^2, while rotational kinetic energy is due to rotational motion, given by KE_rot = (1/2)Iω^2.

Front

Define the term 'elliptical orbit' in the context of celestial mechanics.

Back

An elliptical orbit is a closed path around a central body where the distance between the orbiting body and the central body varies, characterized by two focal points, one of which is occupied by the central body.