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1. Rotational Motion:

Rotational motion is just the motion where something rotates around an axis (like a spinning wheel or a rotating Earth). Think about how a basketball spins when you throw it. The basketball moves in a circular motion around a central point (the center of the ball). That’s rotational motion.

2. Torque:

Torque is a force that causes something to rotate. Imagine you’re using a wrench to loosen a bolt. The harder you push on the wrench, or the farther from the bolt you push, the more torque you create. It’s like twisting a doorknob—if you push it from the side, it opens, but if you push it from the top, you won’t get as much turning force (torque).

• In simple terms: Torque is like the “twist” that makes things spin.

Mathematically, torque (τ) is calculated by the formula:

$$\tau =F\times r\times \sin (\theta )$$ $$tau = F times r times sin(theta)$$ 

Where:

• 
  $F$ is the force,
• 
  $r$ is the distance from the axis of rotation,
• 
  $theta$ is the angle between the force and the lever arm (the distance from the axis of rotation).

3. Angular Velocity:

Angular velocity tells you how fast something is spinning. It’s like speed, but for rotation. If you think about the second hand on a clock, it moves at a certain speed around the clock face. The angular velocity measures how much the angle (or how much rotation) changes per unit of time.

• In simple terms: Angular velocity is the “speed” of rotation.

It’s usually measured in radians per second (rad/s), where one radian is about 57.3 degrees. If a wheel is spinning 360 degrees (or

$2pi$radians) in 1 second, its angular velocity is

$2pi$rad/s.

4. Moment of Inertia:

Moment of inertia is like mass, but for rotating objects. Just like how mass resists linear motion (you feel heavier when you lift something big), the moment of inertia resists rotational motion. It depends on how the mass of an object is distributed relative to the axis of rotation. For example, it’s harder to spin a heavy wheel with mass at the edges than one with mass concentrated at the center.

• In simple terms: Moment of inertia tells you how much an object resists being rotated. The farther the mass is from the axis, the higher the moment of inertia.

For example:

• A solid disk and a ring of the same mass, but with the mass at the edges, will have different moments of inertia. The ring will be harder to spin than the disk.

Mathematically, the moment of inertia

$I$for different shapes can be calculated using specific formulas. For a simple solid disk rotating around its center, it’s:

$$I = frac{1}{2} M R^2$$ 

Where:

• 
  $M$ is the mass of the object,
• 
  $R$ is the radius of the object.

5. Rotational Energy:

Just like how an object moving in a straight line has kinetic energy (energy of motion), a rotating object has rotational kinetic energy. The faster it spins and the more mass it has, the more rotational energy it has.

• In simple terms: Rotational energy is the energy stored in a rotating object.

The formula for rotational kinetic energy (

$K_{text{rot}}$) is:

$$K_{text{rot}} = frac{1}{2} I omega^2$$ 

Where:

• 
  $I$ is the moment of inertia,
• 
  $omega$ is the angular velocity.

Summary :

Imagine you’re spinning a merry-go-round:

• Torque is the force you apply to make it spin.
• Angular velocity tells you how fast it’s spinning.
• Moment of inertia describes how easy or hard it is to spin based on its mass and shape.
• Rotational energy is the energy the merry-go-round has due to its rotation.

When you apply a force (torque), the merry-go-round will start spinning faster (increase angular velocity). How fast it can spin depends on how its mass is distributed (moment of inertia). The faster it spins, the more rotational energy it has.