# Centripetal force, rotary motion, angular velocity, apparent force.

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1 Related Topics Centripetal force, rotary motion, angular velocity, apparent force. Principle and Task A body with variable mass moves on a circular path with ad-justable radius and variable angular velocity. The centrifugal force of the body will be measured as a function of these para-meters. Problems Determination of the centrifugal force as a function 1. of the mass, 2. of the angular velocity, 3. of the distance from the axis of rotation to the centre of gravity of the car. Fig. 1: Experimental set-up for the measurement of centrifugal force. 1

2 Theory and evaluation In the reference system which rotates with the angular velocity vr, the equation of motion of a mass point (mass m, position vector ) reads:.(1) The external force field U (gravitational field) is compensated by the track, the angular velocity is constant, and the car is at rest in the rotating reference system (U = 0; = const. = 0; = const.). From (1), there only remain the centrifugal force and the compensating force, which is read on a spring balance: Since, it follows that Note The spring balance used to measure the centrifugal force follows Hooke s law: = k r, where k is the spring constant. Since the centrifugal force is also linear with respect to r: a distinction must be made between three cases: 1. Stable condition for k > 2. Neutral condition for k = 3. Unstable condition for k <. For safety reasons, the unstable condition should be avoided in the experiment. Also, the range k mv2 is unsuitable for the measurement because of the inaccuracies which occur. 2

4 Fill the table T (s) (N) (N) Determination of the centrifugal force as the function of distance of the axis of the rotational centre The mass of experimental car remains constant. A fixed angular velocity is set to the motor. The radius of the orbit r of the measuring car is increased by means of displacement of the spring balance and the respective centrifugal force Fz and the radius r are measured. Fig. 2: Mass m, at rest in the rotating reference system. 4

5 Fill the table T (s) r ( cm ) (N) (N) Determination of the centrifugal force as the function of the mass of the measuring car. The mass of experimental car is increased. A fixed angular velocity is set to the motor. A predetermined radius (e.g. r = 20 cm) is marked with a piece of adhesive tape and the respective centrifugal force Fz and the mass m are measured. Fill the table T (s) m ( g ) (N) (N) 5

6 Results and discussion Compare and, calculate percent error and draw -F T (s) (N) (N) Error = 6

7 Compare and, calculate percent error and draw -F T (s) r ( cm ) (N) (N) Error = 7

8 Compare and, calculate percent error and draw -F T (s) m ( g ) (N) (N) Error = 8

9 Discuss the results 9

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