Uniform Circular Motion Uniform Circular Motion An object moving in a circle (or part of a circle) with constant speed is said to be undergoing Uniform Circular Motion (UCM).

Centripetal AccelerationCentripetal Acceleration (a(acc))(Radial Acceleration)(Radial Acceleration)

Even though the object has constant speed, it is accelerating as its velocity is constantly changing in direction. Its acceleration is always heading towards the center of the circle and has a magnitude of:

Though constantly changing in direction, the velocity is always perpendicular to the radius.

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Centripetal ForceCentripetal Force ((FFcc))The force producing the centripetal acceleration experienced by the object is the Centripetal Force.

It is the centripetal force that is ultimately responsible for the uniform circular motion.

Centrifugal ForceCentrifugal Force ((FFcfcf))Whenever an object moves in a circular path, it always experiences an outward-seeking force called Centrifugal Force.

The centrifugal force is the partnerof the centripetal force. It cancels out the other forces applied or experienced by the object and ensures that the centripetal force is the only force left.

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Example 1Example 1A stone with a mass of 0.80kg is attached to one end of a string 0.90m long. The string will break if its tension exceeds 600N. The stone is whirled in a horizontal circle on a frictionless table top; the other end of the string is kept fixed. Find the maximum speed the stone can attain without breaking the string.

In side view:

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Example 2Example 2A flat (unbanked) curve on a highway has a radius of 220m. An ambulance rounds the curve at a speed of 25.0m/s. What is the minimum coefficient of static friction that will prevent sliding?

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Example 3Example 3Suppose it is raining in Example 2 such that the road is very slippery (i.e. almost frictionless). The road must be banked in order to prevent slipping. What should be the banking angle of the road?

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Example 4Example 4A small button placed on a horizontal rotating platform with diameter 0.320m will revolve with the platform when the platform is brought up to a speed of 40.0rev/min, provided the button is no more than 0.150m from the axis. What is the coefficient of static friction between the button and the rotating platform?

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Example 5Example 5A statue of a cow is being lifted from the back of a truck to be mounted on a fountain in a park. A steel cable, 10m long, has been attached to the statue. In transferring the statue, it is swung around such that the steel cable makes a 10 vertical axis. What is the speed of the statue?

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Example 6Example 6A bowl of stewed vegetables and meat is swung in a vertical circle using a 1-m long rope. What should be the speed of a the bucket if none of the stew is to be spilled?

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