FORCE

Force is a physical quantity that can change the state of motion or shape of an object. In the CGS (Centimeter-Gram-Second) system, the unit of force is the dyne, while in the SI (International System of Units), it's the newton.

- CGS unit: 1 dyne = 1 gram * centimeter / second^2

- SI unit: 1 newton = 1 kilogram * meter / second^2

The dimension of force is mass times acceleration (M * L / T^2).

For example, when you push a book across a table, you apply a force to it. This force is what causes the book to move.

DIFFERENCE BETWEEN LINEAR DISPLACEMENT AND ANGULAR DISPLACEMENT

Linear displacement refers to the change in position of an object along a straight path, typically measured in units such as centimeters (cm), meters (m), or kilometers (km). The SI (CGS) unit for linear displacement is the centimeter (cm).

Angular displacement, on the other hand, refers to the change in orientation or angle of an object as it moves around a circular path. It is measured in units such as radians (rad) or degrees (°). The SI (CGS) unit for angular displacement is the radian (rad).

Formula:

1. Linear displacement (d) = final position - initial position

2. Angular displacement (θ) = final angle - initial angle

Example:

Let's say a car travels from an initial position of 10 cm to a final position of 30 cm. The linear displacement would be:

Linear displacement (d) = 30 cm - 10 cm = 20 cm

Now, let's consider a wheel rotating from an initial angle of 45° to a final angle of 135°. The angular displacement would be:

Angular displacement (θ) = 135° - 45° = 90°

Both linear and angular displacement describe changes in position, but in different contexts - linear for straight-line motion and angular for rotational motion.

DIFFERENCE BETWEEN KINETIC ENERGY AND POTENTIAL ENERGY :

DIFFERENCE BETWEEN KINETIC ENERGY AND POTENTIAL ENERGY :

1. **Definition**:

   - Kinetic Energy: Energy possessed by an object due to its motion.

   - Potential Energy: Energy possessed by an object due to its position or configuration.

2. **Example**:

   - Kinetic Energy: A moving car has kinetic energy because it's in motion.

   - Potential Energy: A stretched spring has potential energy due to its position; a ball held above the ground has gravitational potential energy.

3. **Unit**:

   - Kinetic Energy: Joules (J).

   - Potential Energy: Joules (J).

4. **Dimension**:

   - Kinetic Energy: [M][L]^2[T]^-2 (Mass × Length^2 × Time^-2)

   - Potential Energy: [M][L]^2[T]^-2 (Mass × Length^2 × Time^-2)

Both kinetic and potential energy have the same dimensions because they are both measures of energy, which has the dimensions [M][L]^2[T]^-2.

DIFFERENCE BETWEEN LINEAR MOMENTUM AND ANGULAR MOMENTUM

Linear momentum and angular momentum are both fundamental concepts in physics, but they represent different aspects of motion.

1. **Linear Momentum:**

   - **Definition:** Linear momentum is the product of an object's mass and its velocity. It represents the quantity of motion in a straight line.

   - **Formula:** Linear momentum = (mass) (velocity), typically denoted as 

     p = mv .

   - **SI Unit:** Kilogram meter per second (kg m/s).

   - **CGS Unit:** Gram centimeter per second (g cm/s).

   - **Dimension:** \([M] \cdot [L] \cdot [T]^{-1}\) (Mass × Length × Time\(^{-1}\)).

   - **Example:** A car moving with a mass of 1000 kg at a velocity of 20 m/s has a linear momentum of 1000 * 20 = 20000 kg m.

2. **Angular Momentum:**

   - **Definition:** Angular momentum is a measure of the rotational motion of an object around an axis. It depends on both the object's rotational inertia (moment of inertia) and its angular velocity.

   - **Formula:** \( \text{Angular momentum} = \text{moment of inertia} \times \text{angular velocity} \), typically denoted as \( L = I\omega \).

   - **SI Unit:** Kilogram meter squared per second (kg m\(^2\)/s).

   - **CGS Unit:** Gram centimeter squared per second (g cm\(^2\)/s).

   - **Dimension:** \([M] \cdot [L]^2 \cdot [T]^{-1}\) (Mass × Length\(^2\) × Time\(^{-1}\)).

   - **Example:** A rotating bicycle wheel with a moment of inertia of 2 kg m\(^2\) and an angular velocity of 10 rad/s has an angular momentum of \(2 \times 10 = 20 \, \text{kg m}^2/\text{s}\).

In summary, linear momentum relates to straight-line motion, while angular momentum relates to rotational motion. They have different formulas, units, and dimensions reflecting their distinct characteristics.

DIFFERENCE BETWEEN LINEAR VELOCITY AND ANGULAR VELOCITY

Different between linear velocity and angular velocity :

Linear velocity refers to the rate of change of an object's position along a straight path, typically measured in units such as meters per second (m/s) or kilometers per hour (km/h). 

Angular velocity, on the other hand, refers to the rate of change of an object's angular position around a fixed point or axis, typically measured in units such as radians per second (rad/s) or degrees per second (°/s). 

In simpler terms, linear velocity deals with motion along a straight line, while angular velocity deals with rotation around a point or axis.

DIFFERENCE BETWEEN DISTANCE AND DISPLACEMENT

1. **Distance**: Distance refers to the total length traveled by an object regardless of its direction. It is a scalar quantity, meaning it only has magnitude. For example, if you walk around a park in a circular path, the distance traveled is the total length of the path you took.

2. **Displacement**: Displacement, on the other hand, refers to the change in position of an object from its initial position to its final position. It includes both the distance between the initial and final positions and the direction from the initial position to the final position. Displacement is a vector quantity because it has both magnitude and direction. For example, if you walk around a park in a circular path and end up at your starting point, your displacement is zero because you've returned to your initial position, even though the distance you traveled may be nonzero.

MOST IMPORTANT DEFINITION :

Explanations of each concept:

1.**Distance**: Distance is the total length of the path traveled by an object, regardless of direction. It's a scalar quantity and doesn't consider direction.

2. **Displacement**: It refers to the change in position of an object, typically measured in a straight line from the initial position to the final position. It has both magnitude (how far an object has moved) and direction.

3. **Velocity**: Velocity is the rate of change of displacement. It's a vector quantity, meaning it has both magnitude (speed) and direction. Mathematically, velocity is expressed as the change in displacement divided by the time taken.

4. **Acceleration**: Acceleration is the rate of change of velocity. Like velocity, it's also a vector quantity and can be positive (speeding up), negative (slowing down), or changing direction. Acceleration can be calculated by dividing the change in velocity by the time taken.

5. **Force**: Force is a push or pull that can cause an object with mass to change its velocity (accelerate). It's also a vector quantity, meaning it has both magnitude and direction. The standard unit of force is the Newton (N). According to Newton's second law of motion, force equals mass times acceleration (F = ma).

Sure, here are explanations for each term:

6. **Linear Momentum**: Linear momentum is a measure of the motion of an object. It is defined as the product of an object's mass and its velocity. Mathematically, linear momentum (p) is expressed as ( p = mv ), where  m is the mass of the object and  v is its velocity. Like velocity, linear momentum is a vector quantity, meaning it has both magnitude and direction. According to the principle of conservation of momentum, the total momentum of a closed system remains constant if no external forces act on it.

7. **Kinetic Energy**: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass of the object and its velocity. Mathematically, kinetic energy (KE) is expressed as ( KE = 1/2mv^2 ), where m  is the mass of the object and  v is its velocity. Kinetic energy is a scalar quantity and is always non-negative.

8. **Potential Energy**: Potential energy is the energy possessed by an object due to its position or configuration. It depends on the position of an object within a force field or a configuration of interacting objects. There are different types of potential energy, such as gravitational potential energy, elastic potential energy, and electric potential energy. Gravitational potential energy (PE) near the surface of the Earth is commonly expressed as ( PE = mgh ), where  m  is the mass of the object,  g  is the acceleration due to gravity, and h  is the height above a reference point. Potential energy is also a scalar quantity.