Answer
1. Static Equilibrium vs. Dynamic Equilibrium:
Static Equilibrium:
- Static equilibrium occurs when an object is at rest and remains at rest, with no net external forces acting on it.
- In static equilibrium, the sum of the forces acting on the object is zero (ΣF = 0), and the sum of the torques (rotational forces) is also zero (Στ = 0).
- An example of static equilibrium is a book sitting on a table.
Dynamic Equilibrium:
- Dynamic equilibrium occurs when an object is in motion but maintains a constant velocity with no net acceleration.
- In dynamic equilibrium, the sum of the forces acting on the object is zero (ΣF = 0), and the sum of the torques (rotational forces) is also zero (Στ = 0).
- An example of dynamic equilibrium is a car moving at a constant speed on a straight road.
2. Linear Acceleration vs. Angular Acceleration:
Linear Acceleration:
- Linear acceleration refers to the change in an object's velocity with respect to time in a straight line.
- It is measured in units like meters per second squared (m/s²).
- Linear acceleration can be either positive (when an object is speeding up) or negative (when an object is slowing down).
- Formula for linear acceleration: a = Δv / Δt, where "a" is acceleration, "Δv" is the change in velocity, and "Δt" is the change in time.
Angular Acceleration:
- Angular acceleration refers to the change in an object's angular velocity with respect to time as it rotates about an axis.
- It is measured in units like radians per second squared (rad/s²).
- Angular acceleration can be either positive (when an object is increasing its rotational speed) or negative (when an object is decreasing its rotational speed).
- Formula for angular acceleration: α = Δω / Δt, where "α" is angular acceleration, "Δω" is the change in angular velocity, and "Δt" is the change in time.
In summary, static equilibrium refers to a state where an object is at rest and has no net forces or torques acting on it, while dynamic equilibrium refers to a state where an object is in motion with a constant velocity and no net forces or torques. Linear acceleration involves changes in an object's straight-line velocity, while angular acceleration involves changes in an object's rotational velocity as it spins or rotates about an axis.
Work Step by Step
1. Static Equilibrium vs. Dynamic Equilibrium:
Static Equilibrium:
- Static equilibrium occurs when an object is at rest and remains at rest, with no net external forces acting on it.
- In static equilibrium, the sum of the forces acting on the object is zero (ΣF = 0), and the sum of the torques (rotational forces) is also zero (Στ = 0).
- An example of static equilibrium is a book sitting on a table.
Dynamic Equilibrium:
- Dynamic equilibrium occurs when an object is in motion but maintains a constant velocity with no net acceleration.
- In dynamic equilibrium, the sum of the forces acting on the object is zero (ΣF = 0), and the sum of the torques (rotational forces) is also zero (Στ = 0).
- An example of dynamic equilibrium is a car moving at a constant speed on a straight road.
2. Linear Acceleration vs. Angular Acceleration:
Linear Acceleration:
- Linear acceleration refers to the change in an object's velocity with respect to time in a straight line.
- It is measured in units like meters per second squared (m/s²).
- Linear acceleration can be either positive (when an object is speeding up) or negative (when an object is slowing down).
- Formula for linear acceleration: a = Δv / Δt, where "a" is acceleration, "Δv" is the change in velocity, and "Δt" is the change in time.
Angular Acceleration:
- Angular acceleration refers to the change in an object's angular velocity with respect to time as it rotates about an axis.
- It is measured in units like radians per second squared (rad/s²).
- Angular acceleration can be either positive (when an object is increasing its rotational speed) or negative (when an object is decreasing its rotational speed).
- Formula for angular acceleration: α = Δω / Δt, where "α" is angular acceleration, "Δω" is the change in angular velocity, and "Δt" is the change in time.
In summary, static equilibrium refers to a state where an object is at rest and has no net forces or torques acting on it, while dynamic equilibrium refers to a state where an object is in motion with a constant velocity and no net forces or torques. Linear acceleration involves changes in an object's straight-line velocity, while angular acceleration involves changes in an object's rotational velocity as it spins or rotates about an axis.
