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: