Kinematics of uniform circular motion

Physics> Kinematics of Uniform Circular Motion

Uniform circular motion (RCM) – movement along a circular path with a stable speed.

Learning challenge

• Combine centripetal force and centripetal acceleration with RKD.

Key points

• With RCD, angular and linear values ​​have a simple relationship. The arc length is proportional to the angle of rotation and the radius. Moreover, v = rω.
• The acceleration responsible for the RVC is referred to as centripetal acceleration. Expressed in the formula a_c = rω² =.
• Any pure force that creates circular motion is called centripetal. Its direction is located in the center of curvature, and the value is equal to m () = mrω²…

Term

• Centripetal – upward.

Angular values

With uniform circular motion, angular and linear quantities are endowed with simple relationships. When objects rotate around some axis, each point of the object follows an arc of a circle. The angle of rotation displays the amount of rotation and is similar to a linear distance. The angle of rotation Δθ can be determined as the ratio of the arc length to the radius of curvature:

The radius of the circle rotates around the angle Δθ. The arc length Δs is described along a circle

From the relation s (Δs = rΔθ) we see:

If we consider the motion in a circular orbit, we will notice that the angular velocity remains stable. Acceleration is written as:

This acceleration is called centripetal.

Centripetal force

Any force or their combination can lead to centripetal or radial acceleration. These will be the rope tension, the Earth’s gravity for the Moon, the friction between skates and ice, etc.

Any pure force that leads to an RVC is called a centripetal force. Its direction is located in the center of curvature, as in centripetal acceleration. Newton’s second law says that pure force is mass acceleration. For uniform circular motion, acceleration is centripetal – a = a_c… Therefore, the magnitude of the centripetal force is equal to:

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