The Earth’s angular velocity around the Sun changes by just under 1 degree per day. Angular acceleration depends on the reference point and is a vector quantity. Angular analogues exist for all linear quantities in Newtonian mechanics, and angular acceleration can be related to linear acceleration in certain settings.
The Earth completes a full circle around the Sun, 360 degrees (2π radians), every 365.24 days. This means that the angle formed by an imaginary line connecting the Earth to the Sun changes by just under 1 degree (π/180 radians) per day. Scientists use the term angular velocity to describe the motion of such an imaginary line. The angular acceleration of an object is equal to the speed at which this speed changes.
Angular acceleration depends on the chosen reference point. An imaginary line connecting the Earth to the Sun changes its angular velocity much more slowly than an imaginary line connecting the Earth to the center of the galaxy. When talking about angular acceleration, it is not necessary for the object in question to travel a complete path around the reference point. One can discuss the change in angular velocity of one car relative to another or a hydrogen atom vibrating relative to the largest oxygen atom in a water molecule.
In physics jargon, acceleration is always a vector quantity regardless of whether it is linear or angular. If a car moving to the right at a speed of 33 feet/second (10 m/s) hits the brakes and stops after 2 seconds, a scientist would describe the car’s average linear acceleration as ft/s2 ( m/ s2). When describing angular acceleration, counterclockwise motion is considered positive and clockwise rotation is negative.
Scientists use the Greek letter alpha, α, to denote angular acceleration. By convention, vectors are bold, and their scalar values are indicated using non-bold typefaces. Thus, α refers to its magnitude. Angular acceleration can be written in the components as a, b, c>, where a is the angular acceleration around the x axis, b is the acceleration around the y axis, and c is the acceleration around the z axis.
All linear quantities used to describe objects or systems in Newtonian mechanics have angular analogues. The angular version of Newton’s famous F=ma is τ = Iα, where τ is the torque and I is the moment of inertia of the system. These last two quantities are respectively the angular equivalents of force and mass.
In certain settings, the angular acceleration of a system about an axis is related to the linear acceleration of the system in space. For example, the distance a ball travels in a given time is related to how fast its outer surface rotates about its center, as long as it is assumed that the ball does not skid or slide. Thus the linear velocity of the ball, s, must be related to the angular velocity ω by the formula s=ωr, where r is the radius of the ball. Thus, the size of the linear acceleration must be related to α by a= αr.
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