All Flashcards
What are the key differences between translational and rotational equilibrium?
Translational Equilibrium: Constant linear velocity, zero net force. | Rotational Equilibrium: Constant angular velocity, zero net torque.
Compare Newton's First Law for linear motion and rotational motion.
Linear Motion: An object maintains constant velocity unless acted upon by a net force. | Rotational Motion: An object maintains constant angular velocity unless acted upon by a net torque.
Compare Newton's Second Law for linear motion and rotational motion.
Linear Motion: Net force equals mass times acceleration (). | Rotational Motion: Net torque equals moment of inertia times angular acceleration ().
Compare force and torque.
Force: A linear push or pull. | Torque: A rotational 'twist' or turning force.
Compare linear and angular acceleration.
Linear Acceleration: The rate of change of linear velocity. | Angular Acceleration: The rate of change of angular velocity.
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 are the steps to solve rotational equilibrium problems?
- Draw free-body and torque diagrams. 2. Identify a convenient pivot point. 3. Calculate the torque produced by each force. 4. Apply the equilibrium condition (Στ = 0).
How do you calculate torque?
- Identify the force (F) causing the rotation. 2. Determine the distance (r) from the pivot point to the point where the force is applied. 3. Find the angle (θ) between the force vector and the lever arm. 4. Calculate torque using the formula τ = rFsinθ.
How do you determine if a system is in rotational equilibrium?
- Identify all forces acting on the object. 2. Calculate the torque produced by each force about a chosen pivot point. 3. Sum all the torques. 4. If the sum of the torques is zero (Στ = 0), the system is in rotational equilibrium.
What are the steps to apply Newton's Second Law for Rotation?
- Calculate the net torque (Στ) acting on the object. 2. Determine the object's moment of inertia (I) about the axis of rotation. 3. Use the equation Στ = Iα to solve for the angular acceleration (α).
How do you apply the conservation of angular momentum?
- Identify the system and ensure no external torques are acting on it. 2. Calculate the initial angular momentum (L_initial = I_initial * ω_initial). 3. Calculate the final angular momentum (L_final = I_final * ω_final). 4. Set L_initial = L_final and solve for the unknown variable.