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What are the differences between rotational and translational kinetic energy?
Rotational: Energy due to rotation, depends on moment of inertia and angular velocity. Translational: Energy due to linear motion, depends on mass and linear velocity.
What are the differences between scalar and vector quantities?
Scalar: Magnitude only (e.g., rotational kinetic energy). Vector: Magnitude and direction (e.g., angular velocity, angular momentum).
What are the differences between moment of inertia for a solid sphere and a hollow sphere?
Solid Sphere: $I = (2/5)MR^2$ (mass concentrated closer to the center). Hollow Sphere: $I = (2/3)MR^2$ (mass distributed further from the center).
What are the differences between rolling with slipping and rolling without slipping?
Rolling without slipping: $v = Rω$ (linear and angular velocities are related). Rolling with slipping: $v ≠ Rω$ (linear and angular velocities are independent).
What are the differences between angular momentum and rotational kinetic energy?
Angular Momentum: Vector quantity, measures the quantity of rotation. Rotational Kinetic Energy: Scalar quantity, measures the energy of rotation.
What is Rotational Kinetic Energy?
Energy an object possesses due to its rotation.
Define Rotational Inertia (I).
How hard it is to change an object's rotation.
Define Angular Velocity (ω).
How fast an object is spinning.
What is a rigid system?
A system where the distance between any two points remains constant.
What is Translational Kinetic Energy?
Energy an object possesses due to the motion of its center of mass.
What happens when a torque is applied to a rotating object?
The rotational kinetic energy of the object changes (Work-Energy Theorem).
What is the effect of increasing the angular velocity of an object?
The rotational kinetic energy increases (quadratically).
What happens if a rolling object's initial potential energy is converted into both translational and rotational kinetic energy?
The object's linear speed at the bottom of the incline will be less than if all potential energy was converted to translational kinetic energy.
What is the effect of increasing the moment of inertia of a rotating object?
The rotational kinetic energy increases, assuming angular velocity remains constant.
What happens when non-conservative forces (e.g., friction) are present in a rotational system?
Total mechanical energy (including rotational kinetic energy) is not conserved.