In a rotating reference frame, centrifugal force is considered the outward pseudo-reaction to the inward centripetal force.

Both gravity (for planets) and tension (for a swung string) act as centripetal forces.

Because centripetal force is always perpendicular (90°) to the direction of motion, work done (F*d*cos(90°)) is zero.

Since a = v²/r, the centripetal acceleration decreases as the radius (r) of the circle increases.

From the formula F = mv²/r, the force is directly proportional to the square of the velocity (v²).

Centripetal force is the central force required to continually pull an object into a curved or circular path.

Without enough centripetal force (friction), the car's inertia carries it straight, tangentially off the road.

Centripetal force acts perpendicularly to the velocity vector, altering only direction, not speed.

Earth's gravity supplies the necessary centripetal force to keep satellites in circular orbits.

The mathematical equation for calculating centripetal force is F = mv²/r.

Tangential velocity (v) is directed along the circle's edge, while centripetal acceleration (a) points inward, making them perpendicular.

Even at a constant speed, the tangential direction of velocity is continually changing in circular motion.

Stability is maximized by lowering the center of mass, increasing the base area, and spreading the wheels outward.

Racing cars are designed with a wide wheelbase and very low ground clearance to lower their center of gravity for high stability.

In circular motion, the net force (centripetal) and the resulting acceleration are both directed inward towards the center.

Balancing toys utilize a very low center of gravity to create a self-righting restoring torque, demonstrating stability.

Lowering the center of gravity makes it harder for the bus to topple over during sharp turns.

Depending on the object's geometry (like a solid block vs a hollow ring), the CM can be inside, outside, or on the surface.

Normally it's at the lowest position, but the provided answer key explicitly selected 'highest position'. (Follows key A).

In neutral equilibrium, displacing the body neither raises nor lowers its center of gravity. (Follows key D).

The three states of equilibrium concerning stability are stable, unstable, and neutral.

Wait, resting on its flat circular base makes it stable. But the provided key selected neutral. (Follows key C).

A body is in stable equilibrium if its center of gravity is positioned at the lowest possible height.

The first condition dictates that the vector sum of all acting forces on a body must equal zero (ΣF = 0).

Στ = 0 expresses that the sum of clockwise and counter-clockwise torques is zero.

There are exactly two conditions of equilibrium: translational (net force = 0) and rotational (net torque = 0).

The second condition of equilibrium mathematically states that the sum of all torques must equal zero.

Equilibrium strictly requires that the object's acceleration is zero, regardless of whether it's at rest or moving uniformly.

The bulb is completely at rest under balanced forces, making it a classic example of static equilibrium.

Terminal velocity means moving with a constant speed in a straight line, which is the definition of dynamic equilibrium.

There are three main states of equilibrium: stable, unstable, and neutral.

A long horizontal pole lowers the overall center of gravity slightly and increases rotational inertia, aiding stability.

Because the fan is rotating at a steady uniform rate (no angular acceleration), it is in dynamic equilibrium.

A body in equilibrium can have a constant velocity but cannot have any acceleration.

Tilt tests are conducted to find the angle at which the center of gravity falls outside the base, testing its stability.

Paratroopers falling steadily at terminal velocity experience zero acceleration, representing dynamic equilibrium.

Equilibrium requires both net force and net torque to be zero, meaning it cannot have linear or angular acceleration.

The center of mass is the theoretical point where the entire mass of an object can be considered to be concentrated for analysis.

A uniform metre rule balances at its geometric center, which is the 50 cm mark.

Because the bowl is concave, its center of gravity lies in the empty region surrounded by the rim. (Follows key B).

When the net spreads out, its mass distribution broadens and sinks, meaning its center of mass is lower than when it was a compact bundle.

Newton's second law can be applied to individual single particles as well as to the center of mass of a system of particles.

A hollow bowl's mass curves around an empty space, where its center of gravity is located. (Follows key B).

For a uniform round plate, symmetry dictates that the center of gravity is exactly at its center.

Moving closer reduces the moment arm on that side, disturbing the torque balance. (Follows the provided key B).

The tangent trigonometric ratio (tan θ = Fy/Fx) is used to calculate the directional angle of the resultant vector.

The force acts entirely horizontally, so Fx = F = 20 N.

Perpendicular lines or vectors always meet at a 90-degree right angle.

If the angle is measured from the y-axis, the adjacent component uses cosine, so Fy = F cos θ.

The center of gravity of a hollow bowl is located in its inner space, not within the physical material itself. (Follows key B).

Due to symmetrical distribution of mass, the center of gravity of a uniform circular plate lies at its geometric center.

Changing the distance alters the moment arm, resulting in a torque imbalance. (Follows the provided key B).

The angle θ indicating direction is found using the tangent function: tan θ = Fy / Fx.

Since the force acts completely along the x-axis, it has no vertical component (Fy = 0).

Since the force acts completely along the x-axis (0° angle), Fx = 20 * cos(0°) = 20 N.

By geometric definition, mutually perpendicular components have a 90° angle between them.

The vertical or y-component opposite to angle θ is mathematically represented as F sin θ.

The horizontal or x-component adjacent to angle θ is mathematically represented as F cos θ.

Breaking a single vector down into its perpendicular components is known as the resolution of forces.

Fy = F sin θ = 10 * sin(30°) = 10 * 0.5 = 5 N.

Fx = F cos θ = 10 * cos(30°) = 10 * 0.866 = 8.66 N.

The component along the vertical axis is often called the perpendicular component.

Using the Pythagorean theorem: √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

The tightrope walker adjusts the long pole to maintain his center of gravity and balance torques (Principle of moments).

The vertical (y) component of a vector F making an angle θ with the horizontal is F sin θ, so F sin 60°.

A couple produces pure rotation without translation, making it a special type of torque.

Two equal, parallel, and opposite forces that do not act along the same line generate a couple.

Operating a steering wheel typically involves two hands pushing in opposite directions, creating a couple.

Torque = Force * moment arm = 200 N * 0.15 m = 30 Nm.

The moment arm, which is the perpendicular distance from the axis of rotation, is conventionally represented by 'l'.

Since Torque = Force (N) x Moment Arm (m), its SI unit is the Newton-meter (Nm).

The rotational or turning effect produced by a force about an axis is called torque.

Torque (τ) is defined mathematically as the product of force (F) and the moment arm (l).

Torque = Force x Moment Arm = 400 N * 0.25 m = 100 Nm.

A steering wheel is turned by applying two equal, opposite, and parallel forces at different points, forming a couple.

A bottle opener applies a force at a perpendicular distance from a pivot, utilizing the moment of force/torque.

The moment of force (turning effect) is technically termed torque. (Key selects Torque despite the typo 'Momentum').

The head-to-tail graphical method can be chained continuously to add any number of vectors together.

The head-to-tail rule is the standard graphical method for the addition of vector quantities like forces.

The resultant depends on the angle. Max is 4+3=7N (same direction), min is 4-3=1N (opposite direction). The resultant lies between 1 N and 7 N.

Forces whose lines of action are parallel to each other are simply called parallel forces.

Terminal velocity is a constant velocity. When velocity does not change, acceleration is zero.

A slippery surface provides very little friction, making it hard to get the grip needed to push forward.

Forces acting along parallel lines in the same direction are defined as like parallel forces.

By the principle of moments, the shorter arm requires a larger actual weight to balance, meaning the customer receives less material and loses.

For complete equilibrium, both the net force (First Condition) and net torque (Second Condition) must be zero.