The centrifugal force, F depends on mass, radius or rotation and angular speed square

Experiments No. 08

Objective:

To show that the centrifugal force, F depends on mass, radius or rotation and angular speed squared.

Apparatus:

It consists of a rotating head driven bya variable speed motor. On the head is an arm and lever arrangement which bears onto a load cell. The arm and lever arrangement are balanced so that only the force arising from the rotating mass is transmitted to the load cell. Different masses are available.

Theory:

The centrifugal force is an outward force apparent in a rotating reference frame; it does not exist when a system is described relative to an inertial frame of reference. All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to the airliner, to the surface of the Earth, or even to the Sun. A reference frame that is at rest (or one that moves with no rotation and at constant velocity) relative to the "fixed stars" is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame--the calculations are simpler, and descriptions more intuitive. When this choice is made, fictitious forces, including the centrifugal force, arise.

In a rotating reference frame, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to the square of the angular velocity of the frame. This is the centrifugal force.

Procedure:

1. In this experiment we show the relations of centrifugal force with the mass, radius and angular speed. 
2. We increase the mass at the same radius and rotational speed, recording the measured force F.
3.  We keep the rotational speed and mass constant and change the radial position of the mass, recording the measured force F. 
4. Now, we keep the mass and radius constant and increasethe rotational speed/angular velocity, recording the measured force F.

Results

Table(Force and Mass)

Mass m (g)	F  (Kg)	Speed (rpm)	Angular speed (rad/sec)	Radius (mm)	Theoretical force (Kg)

Force and Radius

Mass m (g)	F (Kg)	Speed (rpm)	Angular speed (rad/sec)	Radius (mm)	Theoretical force (Kg)

Force and Rotational speed

Mass m (Kg)	F (Kg)	Speed (rpm)	Angular speed (rad/sec)	Radius (mm)	Theoretical force (Kg)

Calculation:

Mass (m)=

Radius (r)=

Speed(n)=

Angular speed

ῳ=2πn/60

Theoritical force

F=mr ῳ2

Precautions :

Note: at the end of the arm is a small balance weight and wing nut. This must be in place for two reasons.

a)To ensure the system only measures force due to the mass on the arm.

b)To retain the mass on the arm should it accidentally become loose during an experiment.

Conclusion:

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