Calculating speed in circular motion

In summary, the conversation discusses the concept of a whirlygig, where a mass is hung through a tube and another mass spins around to form a circle. The tension force acting on the spinning mass is given, and the length of the string is measured. The question is then raised about the speed of the spinning mass, with the incorrect attempt at solving it. It is pointed out that the tension force is not the centripetal force, and the length of the string is not the radius of the circle that the mass travels. The conversation ends with the question about the angle of the string.
  • #1
Anon2459
1. Homework Statement

A whirlygig is made by hanging a mass, m1 = 386.0 g, through a tube and then spinning another mass, m2 = 198.0 g around so that it forms a circle. When this happens the string makes a small angle with the horizontal as shown in the diagram. If this is done at a specific speed then m1 does not move up or down, for this question assume than m2 is moving at this speed. Also assume that there is no friction between the string and the tube.

Tension force acting on m2 is 3.7828

The length of the string between the tube and m2, l, is measured and found to be 81.3 cm. What is the speed of m2?

Homework Equations



F = m x r^2/r

The Attempt at a Solution


[/B]
3.7828 = 198.0 x V^2/81.3

Where did i go wrong?
 
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  • #2
Two things: (1) The tension force is not the centripetal force (2) The length of the string is not the radius of the circle that m2 travels.

Key: What angle does the string make?
 

1. How do you calculate the speed in circular motion?

To calculate the speed in circular motion, you need to know the distance traveled and the time it takes to travel that distance. Then, you can use the formula v = d/t, where v is the speed, d is the distance, and t is the time.

2. What is the difference between tangential speed and angular speed?

Tangential speed is the linear speed of an object moving in a circular path, while angular speed is the rate at which the object rotates around its axis. Tangential speed is measured in units of distance over time, such as meters per second, while angular speed is measured in units of angle over time, such as radians per second.

3. How does radius affect the speed in circular motion?

The radius of the circular path does not affect the speed in circular motion, as long as the period of the motion remains constant. This is because the speed is determined by the distance traveled and the time taken, which are not affected by the radius. However, a larger radius will result in a larger circumference and therefore a longer distance traveled in one revolution, which would lead to a higher tangential speed.

4. Can the speed in circular motion be constant?

Yes, the speed in circular motion can be constant if the object is moving at a constant tangential speed and the radius of the circular path remains constant. This would result in a constant distance traveled in a given time, and therefore a constant speed.

5. How does centripetal acceleration relate to speed in circular motion?

Centripetal acceleration is the acceleration towards the center of the circular path that keeps an object in circular motion. It is directly proportional to the square of the tangential speed and inversely proportional to the radius. This means that as the speed increases, the centripetal acceleration also increases, and as the radius increases, the centripetal acceleration decreases.

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