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What is Rotational Kinetic Energy?
The energy an object possesses due to its rotation.
Define Rotational Inertia (*I*).
How resistant an object is to changes in its rotation.
Define Angular Velocity (*ฯ*).
How fast the object is rotating, measured in radians per second.
What is Translational Kinetic Energy?
The kinetic energy an object possesses due to its linear motion.
What is the Work-Energy Theorem?
Rotational kinetic energy changes when work is done by a torque.
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: $v = Rฯ$ (linear and angular velocities are related). Rolling with slipping: $v โ Rฯ$ (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 the effect of increasing angular velocity on rotational kinetic energy?
Rotational kinetic energy increases (quadratically).
What happens when a figure skater pulls their arms closer to their body?
Their rotational speed increases due to conservation of angular momentum.
What happens when a rotating object's rotational inertia increases?
Its rotational kinetic energy decreases (if angular velocity remains constant).
What is the effect of applying a constant horizontal force to the center of a cylinder?
The cylinder experiences linear and angular acceleration.
What happens when a solid and hollow sphere are released at the top of an incline?
The solid sphere reaches the bottom first.