Lowering the center of mass of a rolling object increases its stability, making it less likely to tip over.

In the kinetic theory of gases, it is assumed that gas molecules occupy a negligible volume and have negligible mass compared to the volume they occupy.

In the kinetic theory of gases, it is assumed that collisions between gas molecules are perfectly elastic, meaning they conserve kinetic energy.

The speed of one car relative to the other is the sum of their speeds since they are moving towards each other: 50 km/h + 70 km/h = 120 km/h.

The speed of Train B relative to Train A is the sum of their speeds: 90 km/h + 70 km/h = 160 km/h.

The mean free path is defined as the average distance a molecule travels before colliding with another molecule.

According to Newton's second law, if mass is doubled and force remains constant, acceleration will halve (a = F/m).

According to the law of conservation of angular momentum, if no external torque acts on a rigid body, its angular momentum remains constant.

If one of the masses is tripled, the gravitational force also triples, as F is directly proportional to the product of the masses.

If the magnetic field is removed, the induced current stops because there is no longer a change in magnetic flux.

The speed of light decreases when it passes from air into water due to the higher refractive index of water.

In rolling without slipping, the total mechanical energy (potential + kinetic) remains constant due to conservation of energy.

Using F = ma, a = F/m = 12 N / 3 kg = 4 m/s².

The acceleration is maximum at maximum displacement, directed towards the equilibrium position.

Using the formula θ = ω₀t + 0.5αt², where ω₀ = 0, α = 2 rad/s², and t = 5 s, we find θ = 0 + 0.5 * 2 * 5² = 25 rad.

90 degrees is equal to π/2 radians, which is approximately 1.57 radians.

Angular momentum L = mvr = 2 kg × 4 m/s × 3 m = 24 kg·m²/s.

The center of mass of a system of particles is defined as the average position of all the particles in the system, weighted by their masses.

Centripetal acceleration is given by a_c = v²/r = (20 m/s)² / 50 m = 8 m/s².

Centripetal acceleration a_c = rω² = 3 m * (4 rad/s)² = 3 * 16 = 48 m/s².

Centripetal force F = mv²/r = 2 kg * (4 m/s)² / 3 m = 10.67 N.

Pure rolling motion occurs when the point of contact between the rolling object and the surface is at rest relative to the surface, meaning there is no sliding.

The critical angle θc can be calculated using sin(θc) = n2/n1, where n1 is the refractive index of the medium where the light is coming from.

Friction opposes the motion of an object, thus decreasing its acceleration according to Newton's laws.

The induced emf depends on the rate of change of magnetic flux, not directly on the area of the loop in a uniform magnetic field. Therefore, it remains the same if the magnetic field is constant.

According to the inverse square law, increasing the distance between two masses decreases the gravitational force between them.

The moment of inertia increases with the square of the radius, as seen in the formula I = k m r^2, where k is a constant depending on the shape.

Increasing the temperature of a gas increases the average kinetic energy of its molecules, which in turn increases their average speed.

The speed of sound in air increases with an increase in temperature.

On a frictionless surface, no net force is required to maintain constant velocity, so the force is 0 N.