If a particle of mass m is projected at an angle αwith the horizontal, then : (a) the angular mo

If a particle of mass m is projected at an angle αwith the...

If a particle of mass $m$ is projected at an angle $\alpha$ with the horizontal, then :
(a) the angular momentum remains constant
(b) the linear momentum of particle remains constant
(c) total mechanical energy remains constant in the absence of air resistance
(d) all the above

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Key Concepts

Angular Momentum

Angular momentum refers to the rotational analogue of linear momentum, defined as the cross product of a particle’s position vector with its momentum. In systems with a central force where the net external torque is zero, angular momentum is conserved. However, in projectile motion under gravity, if the reference point is not aligned with the line of action of gravity, the external gravitational force produces a torque, meaning that angular momentum is not generally conserved.

Linear Momentum

Linear momentum is the product of an object's mass and velocity and is conserved in an isolated system where no external forces act. In the case of projectile motion, although no horizontal forces are typically acting (idealized air resistance neglected), the vertical component is influenced by gravitational acceleration, leading to a change in the total linear momentum over time.

Mechanical Energy

Mechanical energy in a system is the sum of kinetic and potential energies. In projectile motion without air resistance, gravitational force is conservative, meaning that energy is neither created nor destroyed; it simply converts between kinetic and potential forms. Thus, the total mechanical energy remains constant throughout the motion.

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