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What are the differences between translational and rotational equilibrium?
Translational Equilibrium: Zero net force, constant linear velocity. Rotational Equilibrium: Zero net torque, constant angular velocity.
Compare Free-Body Diagrams and Torque Diagrams.
Free-body diagrams: Show forces acting on an object. Torque diagrams: Show both forces and the resulting torques.
Compare angular velocity and angular acceleration.
Angular Velocity: Rate of change of angular position (ω). Angular Acceleration: Rate of change of angular velocity (α).
Compare linear momentum and angular momentum.
Linear Momentum: Mass in motion (p = mv). Angular Momentum: Rotational inertia in motion (L = Iω).
What are the differences between static and dynamic rotational equilibrium?
Static Rotational Equilibrium: Object is at rest (ω = 0). Dynamic Rotational Equilibrium: Object is rotating with constant angular velocity (ω ≠ 0, but constant).
What is Rotational Equilibrium?
The state where an object maintains a constant angular velocity due to zero net torque.
What is Torque?
The rotational equivalent of force, calculated as $\vec{\tau} = \vec{r} \times \vec{F}$, causing an object to rotate.
What is Angular Velocity?
The rate at which an object rotates or revolves relative to another point, i.e. how many radians per second the object turns.
What is Angular Acceleration?
The rate of change of angular velocity, resulting from a net torque.
Define Moment of Inertia.
A measure of an object's resistance to changes in its rotation rate. Represented by 'I' in rotational dynamics.
What is Newton's First Law for Rotation?
An object maintains a constant angular velocity unless acted upon by a net torque.
What is the effect of a net torque on an object?
A net torque causes angular acceleration, changing the object's angular velocity.
What is the effect of increasing the distance from the pivot point when applying a force?
Increasing the distance (r) increases the torque (τ = rFsinθ), assuming force and angle remain constant.
What happens when a spinning figure skater pulls their arms inward?
Their moment of inertia decreases, causing their angular velocity to increase to conserve angular momentum.
What is the effect of applying a force perpendicular to a rod at its end?
It creates a torque that causes the rod to rotate around the pivot point, resulting in angular acceleration.
What happens when the sum of all torques acting on a system is zero?
The system is in rotational equilibrium, meaning its angular velocity remains constant.
What happens in the absence of external torques?
Angular momentum is conserved.