1st Semester Physics Important Questions

Explanation:
A rotating wheel slows down under a constant opposing torque, which produces uniform angular deceleration. The motion is analyzed using Rotational Dynamics, where the change in angular velocity over time helps determine angular acceleration. The moment of inertia plays a key role here and is found using Mass and radius of gyration. Once angular acceleration is established, torque is linked through the rotational form of Newton’s second law, where torque depends on both moment of inertia and angular acceleration. The conversion of rotational speed from revolutions per minute into radians per second is essential before applying equations. The negative sign conceptually indicates retardation, showing that the motion is slowing down uniformly over the given time interval. The process involves systematically connecting kinematic relations of angular motion with dynamic relations of rotational force. Careful unit conversion and consistent use of angular quantities ensure correct formulation of the governing equation, which ultimately allows determination of the required retarding effect acting on the wheel.

Explanation:
When a rotating disc speeds up, energy is supplied in the form of work which gets stored as rotational kinetic energy. The energy depends on the moment of inertia of the disc and the square of its angular velocity. Since the object is a uniform disc, its inertia is determined from its Mass and radius. The change in rotational speed is converted from revolutions per second into angular velocity using standard conversion involving 2π. The work done is essentially the difference between final and initial rotational kinetic energies. This approach reflects energy conservation in rotational motion, where external work increases the system’s rotational energy. The relationship between angular velocity and kinetic energy is quadratic, meaning small increases in speed significantly affect energy storage. The calculation requires careful substitution of initial and final angular speeds, followed by evaluating the difference in energy states to find the total work supplied during acceleration of the flywheel.

Explanation:
The situation involves conservation of angular momentum for a rotating celestial body. When no external torque acts on the system, the product of moment of inertia and angular velocity remains constant. The Earth, treated as a uniform sphere, has its moment of inertia depending on its Mass and square of its radius. If the radius changes while Mass remains the same, the moment of inertia changes significantly due to its dependence on the square of the radius. A reduction in radius leads to a decrease in moment of inertia, which in turn causes angular velocity to increase to maintain angular momentum conservation. Since the rotational period is inversely related to angular velocity, the duration of rotation changes accordingly. The reasoning involves connecting Rotational Dynamics with conservation principles rather than direct force analysis. The key idea is that redistribution of Mass closer to the axis of rotation increases rotational speed, thereby reducing the time taken for one complete rotation.

Explanation:
In a rotating reference frame, fictitious or pseudo forces arise due to non-inertial effects. These include centrifugal force and Coriolis force, both dependent on the angular velocity of the rotating system. When a particle is stationary relative to the rotating frame, its velocity in that frame is zero. The Coriolis effect depends on the velocity of the particle within the rotating frame, so it does not contribute in this situation. However, the centrifugal effect depends only on the position of the particle relative to the axis of rotation and acts outward regardless of motion. Thus, only position-dependent inertial effects remain relevant. The analysis is based on identifying which pseudo forces depend on velocity and which depend purely on radial distance from the axis. Understanding these distinctions is essential in rotating frame dynamics, where apparent forces replace real inertial forces to describe motion consistently within the non-inertial system.