recall and write the definition of the review vocabulary term.
magnitude

use your book to define each term.
lever arm

torque

moment of inertia

newton’s second law for rotational motion

Question

recall and write the definition of the review vocabulary term.
magnitude

use your book to define each term.
lever arm

torque

moment of inertia

newton’s second law for rotational motion

Accepted Answer

### 1. Definition of magnitude
# Brief Explanations:
In physics (a subfield of Natural Science), magnitude refers to the size or quantity of a physical quantity (like force, velocity, or acceleration), ignoring direction (for vector quantities, it's the scalar value representing the amount). For example, the magnitude of a velocity vector of 5 m/s east is 5 m/s.
# Answer:
In physics, the **magnitude** of a physical quantity (e.g., vector, scalar) is its size or amount, representing the numerical value (and unit) of the quantity (e.g., the magnitude of a force of $ 10\,\text{N} $ north is $ 10\,\text{N} $).

### 2. Definition of lever arm
# Brief Explanations:
In physics (specifically rotational motion), the lever arm (or moment arm) is the perpendicular distance from the axis of rotation to the line of action of a force. It determines how effectively a force produces torque.
# Answer:
The **lever arm** (or moment arm) is the perpendicular distance from the axis of rotation to the line of action of a force (used to calculate torque: $ \tau = F \cdot d_{\perp} $, where $ d_{\perp} $ is the lever arm).

### 3. Definition of torque
# Brief Explanations:
Torque (rotational force) is the measure of a force’s ability to cause rotational motion about an axis. It depends on the force’s magnitude, the lever arm, and the angle between the force and the lever arm ($ \tau = rF\sin\theta $, where $ r $ is the distance from the axis, $ F $ is force, and $ \theta $ is the angle between $ \vec{r} $ and $ \vec{F} $).
# Answer:
**Torque** ($ \tau $) is the rotational equivalent of force, causing angular acceleration. It is defined as $ \tau = rF\sin\theta $ (or $ \tau = F \cdot d_{\perp} $, where $ d_{\perp} $ is the lever arm), where $ r $ is the distance from the axis, $ F $ is the force, and $ \theta $ is the angle between the position vector $ \vec{r} $ and the force vector $ \vec{F} $.

### 4. Definition of moment of inertia
# Brief Explanations:
Moment of inertia ($ I $) is the rotational equivalent of mass, representing an object’s resistance to angular acceleration. It depends on the object’s mass distribution and the axis of rotation ($ I = \sum mr^2 $ for discrete masses, $ I = \int r^2 dm $ for continuous masses).
# Answer:
The **moment of inertia** ($ I $) is a measure of an object’s resistance to changes in its rotational motion. For a system of particles, $ I = \sum m_i r_i^2 $ (where $ m_i $ is the mass of each particle, $ r_i $ is its distance from the axis); for a continuous object, $ I = \int r^2 dm $.

### 5. Definition of Newton’s second law for rotational motion
# Brief Explanations:
Newton’s second law for rotation relates net torque to angular acceleration: $ \sum \tau = I\alpha $, where $ \sum \tau $ is the net torque, $ I $ is the moment of inertia, and $ \alpha $ is the angular acceleration. It is the rotational analog of $ \sum F = ma $.
# Answer:
**Newton’s second law for rotational motion** states that the net torque ($ \sum \tau $) acting on a rigid body equals the product of its moment of inertia ($ I $) and angular acceleration ($ \alpha $): $ \sum \tau = I\alpha $ (analogous to $ \sum F = ma $ for linear motion).

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QUESTION IMAGE

Question

Explanation:

1. Definition of magnitude

Answer:

2. Definition of lever arm