Grade 11 Mechanics Study Notes

Vector

A physical quantity that has both magnitude and direction (e.g., force, velocity, displacement).

Scalar

A physical quantity that has magnitude only (e.g., time, mass, speed, distance).

Resultant Vector

A single vector that produces the same effect as two or more vectors acting together.

Vector Resolution (Horizontal Component)

The component of a vector acting along the horizontal axis, given by R_x = R ok\cos(\theta).

Vector Resolution (Vertical Component)

The component of a vector acting along the vertical axis, given by $R_y = R\sin(\theta)$.

Normal Force ($N$ or $F_N$)

The perpendicular force exerted by a surface on an object in contact with it.

Maximum Static Friction ($f_{s\,\text{max}}$)

The force that opposes the tendency of motion of a stationary object relative to a surface and represents the threshold to initiate sliding: $f_{s\,\text{max}} = \mu_s N$.

Kinetic Friction ($f_k$)

The force that opposes the motion of a moving object sliding relative to a surface: $f_k = \mu_k N$.

Weight Components on an Inclined Plane

Parallel to slope: $F_{g\parallel} = mg\sin(\theta)$; Perpendicular to slope: $F_{g\perp} = mg\cos(\theta)$.

Newton's First Law of Motion

A body will remain in its state of rest or motion at constant velocity unless a non-zero resultant or net force acts on it.

Newton's Second Law of Motion

When a net force acts on an object, the object accelerates in the direction of the net force; acceleration is directly proportional to the net force and inversely proportional to the mass ($F_{\text{net}} = ma$).

Newton's Third Law of Motion

When object A exerts a force on object B, object B simultaneously exerts an oppositely directed force of equal magnitude on object A.

Newton's Law of Universal Gravitation

Every particle in the universe attracts every other particle with a gravitational force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres: $F = G\frac{m_1 m_2}{r^2}$.

Gravitational Acceleration ($g$)

The acceleration experienced by an object due to gravity near a spherical body's surface: $g = \frac{GM}{r^2}$, which is approximately $9.8\,m\cdot s^{-2}$ on Earth.

Vector

A physical quantity that has both magnitude and direction (e.g., force, velocity, displacement).

Scalar

A physical quantity that has magnitude only (e.g., time, mass, speed, distance).

Resultant Vector

A single vector that produces the same effect as two or more vectors acting together.

Vector Resolution (Horizontal Component)

The component of a vector acting along the horizontal axis, given by $R_x = R ok\cos(\theta)$.

Vector Resolution (Vertical Component)

The component of a vector acting along the vertical axis, given by $R_y = R\sin(\theta)$.

Normal Force ($N$ or $F_N$)

The perpendicular force exerted by a surface on an object in contact with it.

Maximum Static Friction ($f_{s\,\text{max}}$)

The force that opposes the tendency of motion of a stationary object relative to a surface and represents the threshold to initiate sliding: $f<em>{s\,\text{max}} = \mu</em>s N$.

Kinetic Friction ($f_k$)

The force that opposes the motion of a moving object sliding relative to a surface: $f<em>k = \mu</em>k N$.

Weight Components on an Inclined Plane

Parallel to slope: $F<em>{g\parallel} = mg\sin(\theta)$; Perpendicular to slope: $F</em>{g\perp} = mg\cos(\theta)$.

Newton's First Law of Motion

A body will remain in its state of rest or motion at constant velocity unless a non-zero resultant or net force acts on it.

Newton's Second Law of Motion

When a net force acts on an object, the object accelerates in the direction of the net force; acceleration is directly proportional to the net force and inversely proportional to the mass ($F_{\text{net}} = ma$).

Newton's Third Law of Motion

When object A exerts a force on object B, object B simultaneously exerts an oppositely directed force of equal magnitude on object A.

Newton's Law of Universal Gravitation

Every particle in the universe attracts every other particle with a gravitational force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres: $F = G\frac{m<em>1 m</em>2}{r^2}$.

Gravitational Acceleration ($g$)

The acceleration experienced by an object due to gravity near a spherical body's surface: $g = \frac{GM}{r^2}$, which is approximately $9.8\,m\cdot s^{-2}$ on Earth.