UGC NET Physical Education Kinesiology and Biomechanics Syllabus

For a projectile launched and landing at the same height, what release angle gives maximum range, and why?

An angle of $45^{\circ}$ gives maximum range, because it optimally balances the horizontal and vertical components of velocity. The range is $$R = \frac{v^{2}\sin(2\theta)}{g}$$ which is maximised when $\sin(2\theta)=1$, i.e., $\theta = 45^{\circ}$.

Give the formulas for the time of flight and maximum height of a projectile launched at angle $\theta$ with speed $v$.

Time of flight: $$t = \frac{2v\sin\theta}{g}$$ Maximum height: $$H = \frac{v^{2}\sin^{2}\theta}{2g}$$

What is the shape of a projectile's flight path (ignoring air resistance), and how do its horizontal and vertical velocity components behave?

The path is a parabola. The horizontal velocity component remains constant (no horizontal force), while the vertical component decreases on the way up, becomes zero at the peak, and increases on the way down due to gravity.

Define linear kinematics and distinguish distance from displacement.

Linear kinematics describes linear motion without reference to its causes (forces). Distance is the total path length travelled (a scalar); displacement is the straight-line change in position from start to finish in a given direction (a vector).

Distinguish speed from velocity, giving the defining formula for each.

Speed is the rate of covering distance (scalar): $$\text{speed} = \frac{\text{distance}}{\text{time}}$$ Velocity is the rate of change of displacement (vector): $$\vec{v} = \frac{\Delta \vec{s}}{\Delta t}$$

Define linear acceleration and give its formula.

Linear acceleration is the rate of change of velocity with time: $$\vec{a} = \frac{\vec{v}_f - \vec{v}_i}{t}$$ Its SI unit is $m/s^{2}$. Negative acceleration (deceleration) opposes the direction of motion.

Write the three equations of uniformly accelerated linear motion.

$$v = u + at$$ $$s = ut + \tfrac{1}{2}at^{2}$$ $$v^{2} = u^{2} + 2as$$ where $u$ is initial velocity, $v$ final velocity, $a$ acceleration, $t$ time, and $s$ displacement.

Define angular kinematics and the three units used to measure angular displacement.

Angular kinematics describes rotational motion without regard to its causes. Angular displacement can be measured in degrees, radians, or revolutions, where $1$ revolution $= 360^{\circ} = 2\pi$ radians.

Define angular velocity and angular acceleration with their formulas.

Angular velocity is the rate of change of angular displacement: $$\omega = \frac{\Delta\theta}{\Delta t}\ (\text{rad/s})$$ Angular acceleration is the rate of change of angular velocity: $$\alpha = \frac{\Delta\omega}{\Delta t}\ (\text{rad/s}^{2})$$

State the relationship between linear (tangential) velocity and angular velocity, and explain its relevance to a long-handled implement in sport.

$$v = r\omega$$ where $v$ is tangential velocity, $r$ the radius of rotation, and $\omega$ angular velocity. A longer radius (e.g., a longer golf club or tennis racket) produces greater linear velocity at the striking end for the same angular velocity.

Define linear kinetics and the concept of force.

Linear kinetics studies the forces that cause or alter linear motion. A force is a push or pull that tends to change a body's state of rest or motion; it is a vector with magnitude and direction, measured in newtons (N), where $1\ N = 1\ kg\cdot m/s^{2}$.

Define momentum and impulse, and state the impulse-momentum relationship.

Momentum is mass times velocity: $$p = mv$$ Impulse is force times the time over which it acts: $$J = F\cdot t$$ The impulse–momentum theorem states $$F\cdot t = \Delta(mv)$$ i.e., impulse equals the change in momentum (basis of 'following through' to apply force longer).

State the law of conservation of linear momentum.

In the absence of external forces, the total momentum of a system remains constant. For a collision: $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$

Define angular kinetics and the concept of torque (moment of force), including its formula.

Angular kinetics studies the forces (torques) that produce rotation. Torque is the turning effect of a force about an axis: $$\tau = F \times d$$ where $d$ is the perpendicular distance (moment arm) from the axis to the line of action of the force.

Define moment of inertia and state how it depends on mass distribution.

Moment of inertia is a body's resistance to change in its rotational motion: $$I = \sum m r^{2}$$ It increases when mass is distributed farther from the axis (larger $r$). A tucked diver (small $I$) spins faster than an extended diver (large $I$).

State the principle of conservation of angular momentum and apply it to a spinning skater.

With no external torque, angular momentum $$L = I\omega$$ is conserved. When a skater pulls in their arms, moment of inertia $I$ decreases, so angular velocity $\omega$ increases to keep $L$ constant — they spin faster.

Define friction and state the formula relating it to the normal force.

Friction is the force opposing relative motion (or tendency of motion) between two surfaces in contact. $$F_{friction} = \mu N$$ where $\mu$ is the coefficient of friction and $N$ is the normal (perpendicular) reaction force.

Distinguish static, sliding (kinetic), and rolling friction, and rank their typical magnitudes.

Static friction opposes the start of motion and reaches a maximum just before sliding; sliding (kinetic) friction opposes ongoing sliding; rolling friction opposes a body rolling over a surface. Typically: static > sliding > rolling for the same surfaces.

Give one sports example each where friction is increased and where it is decreased deliberately.

Increased: spiked/studded shoes, chalk on gymnasts' hands, and rosin for better grip and traction. Decreased: waxing skis, smooth swimming costumes, and a polished ice surface to reduce resistance and increase speed.

What is spin in sports, and name the main types of spin imparted to a ball.

Spin is rotation imparted to a ball about an axis, affecting its flight and bounce. Main types: top spin, back spin, side spin, and the combination 'check' spin. Spin works through the Magnus effect.

Explain the Magnus effect and how it makes top spin behave.

The Magnus effect is the sideways force on a spinning ball caused by unequal air pressure: air moves faster (lower pressure) on the side spinning with the airflow and slower (higher pressure) on the other. Top spin creates higher pressure above and lower below, producing a downward force that makes the ball dip and drop more sharply, with a faster, lower bounce.

Compare the bounce behaviour of a ball with top spin versus back spin.

Top spin causes the ball to dip quickly and bounce forward low and fast (kicks on). Back spin makes the ball float/stay up longer and, on bouncing, sits up or even bounces backward, slowing down (a 'stop' or 'check').

Define impact and the coefficient of restitution, including its formula.

Impact is a collision between two bodies over a very short time. The coefficient of restitution ($e$) measures the elasticity (bounciness) of an impact: $$e = \frac{\text{velocity of separation}}{\text{velocity of approach}}$$ It ranges from $0$ (perfectly inelastic) to $1$ (perfectly elastic).

Distinguish elastic, inelastic, and perfectly inelastic collisions in terms of the coefficient of restitution.

Perfectly elastic: $e = 1$ (kinetic energy conserved, bodies bounce apart fully); inelastic: $0 < e < 1$ (some kinetic energy lost as heat/sound); perfectly inelastic: $e = 0$ (bodies stick together, maximum energy loss).

How does dropping a ball measure the coefficient of restitution, and how do temperature and surface affect it?

Drop a ball from height $h_1$ and measure rebound height $h_2$; then $$e = \sqrt{\frac{h_2}{h_1}}$$ A warmer ball and a harder/firmer surface generally increase $e$ (higher, livelier bounce); a cold ball or soft surface lowers it.

Define air resistance (drag) and list the factors affecting the drag force on a body in sport.

Air resistance (drag) is the force opposing a body's motion through air. The drag force depends on the body's velocity (greatly, roughly $\propto v^{2}$), frontal surface area, shape/streamlining, smoothness of the surface, and the density of the air.

Explain how streamlining and the role of air density influence performance in sports.

Streamlining (an aerodynamic shape) reduces drag by smoothing airflow and minimising turbulence behind the body, e.g., cyclists' crouched posture and aero helmets. Lower air density (high altitude) reduces drag, aiding sprinting, throwing, and jumping, though it also reduces oxygen availability for endurance events.

State Archimedes' principle and the principle of flotation as applied to swimming.

Archimedes' principle: a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced. By flotation, a body floats when its weight equals the buoyant force; a swimmer floats if their average density is less than that of water (helped by lungs full of air).

In water dynamics, distinguish the buoyant force and drag (water resistance) acting on a swimmer.

Buoyancy is the upward force from displaced water that supports the swimmer and is countered by gravity. Drag is the resistance opposing forward motion through water; it includes form (frontal) drag, surface (skin) drag, and wave drag, all of which a streamlined body position minimises.

Define postural deformities and name the common spinal (vertebral) deformities.

Postural deformities are deviations from the normal alignment of the body that strain muscles and joints. Common spinal deformities are kyphosis (exaggerated outward thoracic curve / round upper back), lordosis (exaggerated inward lumbar curve / hollow back), and scoliosis (lateral S- or C-shaped curvature of the spine).

Distinguish the lower-limb deformities knock-knees, bow legs, and flat foot, and give one corrective exercise for each.

Knock-knees (genu valgum): knees touch but ankles stay apart — corrected by horse riding and using a pillow between the knees. Bow legs (genu varum): knees stay apart when ankles touch — corrected by walking on the inner edges of the feet. Flat foot (pes planus): no arch in the sole — corrected by walking on toes/heels, picking up objects with the toes, and skipping/rope exercises.