While translational motion can accurately describe a point-like object, real-life objects can also rotate. This unit describes the rotational motion of these extended objects.
All objects have a center of mass. This is the point where the force of gravity acts on an object. One can find an object's center of mass by hanging it on a string from two points. The center of mass will be where these lines intersect.
All objects have a center of mass. This is the point where the force of gravity acts on an object. One can find an object's center of mass by hanging it on a string from two points. The center of mass will be where these lines intersect.
Rotational kinematics are very similar to translational kinematics. While the kinematic equations are basically the same, the units are not.
Instead of position (x), rotating objects have angular position (θ) in radians
Instead of velocity (v), rotating objects have angular velocity (ω) in radians/second
Instead of acceleration (a), rotating objects have angular acceleration (α) in radians/second/second.
Instead of position (x), rotating objects have angular position (θ) in radians
Instead of velocity (v), rotating objects have angular velocity (ω) in radians/second
Instead of acceleration (a), rotating objects have angular acceleration (α) in radians/second/second.
https://www.youtube.com/watch?v=fmXFWi-WfyU
Torque is the rotational motion equivalent to a force, or what causes angular acceleration. Torque (τ) is a force applied at a distance and is measured in Newton•meters. Only the component of the force that is perpendicular to the torque arm, or the radius between the axis of rotation and the force contributes to the torque.
Rotational inertia (I) is an object's resistance to angular acceleration, which is dependent on an object's mass and how the mass is distributed throughout the object. While the formula for rotational inertia is different for various objects, it is always proportional to an object's mass and the square of the radius of that mass. For a ring or series of point masses at a radius, the equation is I = mr^2.
Newton's 2nd law of motion also applies to rotation:
Newton's 2nd law of motion also applies to rotation:
Net Torque = Rotational Inertia • Angular Acceleration
Σ τ = I • α
Σ τ = I • α
Just like translationally moving objects, rotating objects possess kinetic energy. This energy can be modeled with the formula:
Kinetic Energy = 1/2 • Rotational Inertia • (Angular velocity)squared
K = 1/2 I • ω^2
K = 1/2 I • ω^2
Just as objects can have linear momentum, rotating objects can have angular momentum (L). An object's angular momentum is the product of its rotational inertia and its angular velocity. An impulse can also change the angular momentum of an object. This impulse (ΔL) is a torque applied for a period of time.
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