The corresponding quantities in rotational motion related to m, `vecF, vecp and vecv` in linear motion are respectively

Options

A. force
B. momentum
C. impulse
D. energy

Answer

To solve the question regarding the corresponding quantities in rotational motion related to mass, force, momentum, and velocity in linear motion, we will identify the rotational analogs for each of these linear quantities step by step.

### Step-by-Step Solution:

1. **Identify the Linear Quantity: Mass (m)**
- In linear motion, mass (m) is a measure of the amount of matter in an object and is a scalar quantity.
- **Rotational Analog:** The rotational analog of mass is **Moment of Inertia (I)**. Moment of inertia quantifies how mass is distributed relative to an axis of rotation and affects how much torque is needed for a desired angular acceleration.

2. **Identify the Linear Quantity: Force (F)**
- In linear motion, force (F) is defined as the interaction that causes an object to change its velocity, according to Newton's second law (F = ma).
- **Rotational Analog:** The rotational analog of force is **Torque (τ)**. Torque is the rotational equivalent of force and is defined as the product of the force and the distance from the pivot point (τ = r × F), where r is the distance from the axis of rotation.

3. **Identify the Linear Quantity: Linear Momentum (p)**
- In linear motion, linear momentum (p) is the product of mass and velocity (p = mv) and represents the quantity of motion an object has.
- **Rotational Analog:** The rotational analog of linear momentum is **Angular Momentum (L)**. Angular momentum is defined as the product of moment of inertia and angular velocity (L = Iω), where ω is the angular velocity.

4. **Identify the Linear Quantity: Velocity (v)**
- In linear motion, velocity (v) is the rate of change of displacement with respect to time.
- **Rotational Analog:** The rotational analog of velocity is **Angular Velocity (ω)**. Angular velocity measures how quickly an object rotates and is defined as the rate of change of angular displacement with respect to time.

### Summary of Corresponding Quantities:
- **Mass (m)** → **Moment of Inertia (I)**
- **Force (F)** → **Torque (τ)**
- **Linear Momentum (p)** → **Angular Momentum (L)**
- **Velocity (v)** → **Angular Velocity (ω)**