What Is Uniform Circular Motion?

The motion of a particle along a circle. If the arcs passing through at any equal time are of equal length, this movement is called "uniform circular motion". Uniform circular motion is the most common and simple motion in circular motion (because speed is a vector, uniform circular motion actually refers to uniform circular motion) ^[1] .

The necessary and sufficient conditions for doing uniform circular motion are ^[2]

Physical quantity describing the speed of uniform circular motion ^[4] :

v Linear velocity of uniform circular motion v

Meaning: A physical quantity describing how fast the particle moves along the arc. The greater the linear velocity, the faster the particle moves along the arc.

Definition: The magnitude of the linear velocity is equal to the ratio of the arc length s passed by the particle to the time t used.

Unit: m / s.

Vector: The direction is in the direction of tangent to each point of the circle.

is the instantaneous speed of the object making a uniform circular motion.

When the particle moves in a uniform circular motion, the linear velocity does not change, but the direction changes at all times.

Constant vector.

The objects connected at the edges have the same linear velocity.

Angular velocity of uniform circular motion

Definition: The ratio of the turning angle of the radius (moving radius) connecting the particle and the center of the circle to the time taken is called the angular velocity of the uniform circular motion.

Unit: rad / s (radian per second).

Vector (not discussed in middle school, use <Ampey's right-hand rule> to determine the direction, for example: when it rotates clockwise on a horizontal plane, the direction of the angular velocity is vertically downward).

The angular velocity is constant when the particle moves in a uniform circular motion.

Any two points on the same object, except for the center of rotation, have the same angular velocity.

T Period of uniform circular motion T

Definition: The time it takes for an object to make a uniform circular motion is called a period.

Unit: s (second).

Scalar: only size, no direction.

Significance: Quantitatively describe the speed of uniform circular motion. When the radii are equal, a long period means slow movement, and a short period means fast movement.

When the particle moves in a uniform circular motion, the period is constant.

f Frequency of uniform circular motion f

Definition: The reciprocal of the period (the number of periodic movements completed per second) is called frequency.

Unit: Hz (Hertz).

Scalar: only size, no direction.

Significance: Quantitatively describe the speed of uniform circular motion. A high frequency indicates a fast movement, and a low frequency indicates a slow movement.

When the particle moves in a uniform circular motion, the frequency is constant.

n Rotation speed of uniform circular motion n

Definition: The number of revolutions per second of a particle making a uniform circular motion.

Unit: r / s (revolutions per second) in the International System of Units; r / min (revolutions per minute) is a common unit. 1 r / s = 60 r / min.

(Note: r = round English: circle)

Scalar: only size, no direction.

Significance: Quantitatively describe the speed of uniform circular motion in practice. A high speed indicates a fast movement, and a low speed indicates a slow movement.

When the particle moves in a uniform circular motion, the rotation speed is constant.