A Ball Is Attached To A String Moving In Uniform Circular Motion. The Radius Of The Motion Is 0.115 M 0.115 \, \text{m} 0.115 M , And The Speed Of The Ball Is 5.00 M/s 5.00 \, \text{m/s} 5.00 M/s .What Is The Period Of Motion For The Ball? T = [ ? ] S T = [?] \, \text{s} T = [ ?] S

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Introduction

When a ball is attached to a string and moves in uniform circular motion, it experiences a constant speed while continuously changing direction. This type of motion is characterized by a circular path with a constant radius. In this scenario, we are given the radius of the motion as 0.115 m0.115 \, \text{m} and the speed of the ball as 5.00 m/s5.00 \, \text{m/s}. Our objective is to calculate the period of motion for the ball, denoted by TT.

Understanding Uniform Circular Motion

Uniform circular motion is a type of motion where an object moves in a circular path at a constant speed. The direction of the object's velocity is constantly changing, resulting in a centripetal acceleration directed towards the center of the circle. This acceleration is necessary to maintain the circular motion and is given by the equation:

ac=v2ra_c = \frac{v^2}{r}

where aca_c is the centripetal acceleration, vv is the speed of the object, and rr is the radius of the circular path.

Calculating the Period of Motion

The period of motion, denoted by TT, is the time taken by the ball to complete one full revolution around the circular path. It is related to the speed of the ball and the radius of the circular path by the equation:

T=2Ï€rvT = \frac{2\pi r}{v}

where TT is the period of motion, rr is the radius of the circular path, and vv is the speed of the ball.

Substituting Given Values

We are given the radius of the motion as 0.115 m0.115 \, \text{m} and the speed of the ball as 5.00 m/s5.00 \, \text{m/s}. Substituting these values into the equation for the period of motion, we get:

T=2π×0.115 m5.00 m/sT = \frac{2\pi \times 0.115 \, \text{m}}{5.00 \, \text{m/s}}

Evaluating the Expression

Evaluating the expression, we get:

T=2π×0.115 m5.00 m/s=0.723 m5.00 m/s=0.145 sT = \frac{2\pi \times 0.115 \, \text{m}}{5.00 \, \text{m/s}} = \frac{0.723 \, \text{m}}{5.00 \, \text{m/s}} = 0.145 \, \text{s}

Conclusion

In conclusion, the period of motion for the ball is 0.145 s0.145 \, \text{s}. This means that the ball takes approximately 0.145 s0.145 \, \text{s} to complete one full revolution around the circular path.

Additional Information

  • The period of motion is a measure of the time taken by the ball to complete one full revolution around the circular path.
  • The period of motion is related to the speed of the ball and the radius of the circular path by the equation T=2Ï€rvT = \frac{2\pi r}{v}.
  • The period of motion is an important concept in physics, particularly in the study of circular motion.

References

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.

Discussion

  • What is the relationship between the period of motion and the speed of the ball?
  • How does the radius of the circular path affect the period of motion?
  • What is the significance of the period of motion in the study of circular motion?

Introduction

In our previous article, we explored the concept of uniform circular motion and calculated the period of motion for a ball attached to a string. In this article, we will address some common questions related to this topic.

Q&A

Q: What is the relationship between the period of motion and the speed of the ball?

A: The period of motion is inversely proportional to the speed of the ball. This means that as the speed of the ball increases, the period of motion decreases, and vice versa.

Q: How does the radius of the circular path affect the period of motion?

A: The radius of the circular path has a direct relationship with the period of motion. As the radius of the circular path increases, the period of motion also increases.

Q: What is the significance of the period of motion in the study of circular motion?

A: The period of motion is an important concept in the study of circular motion. It helps us understand the time taken by an object to complete one full revolution around a circular path.

Q: Can you provide an example of how the period of motion is used in real-life situations?

A: Yes, the period of motion is used in various real-life situations, such as:

  • Calculating the time taken by a satellite to complete one orbit around the Earth.
  • Determining the time taken by a car to complete one lap around a circular track.
  • Understanding the time taken by a planet to complete one rotation around its axis.

Q: How does the period of motion relate to the frequency of rotation?

A: The period of motion and the frequency of rotation are inversely related. As the period of motion increases, the frequency of rotation decreases, and vice versa.

Q: Can you provide a formula to calculate the period of motion?

A: Yes, the formula to calculate the period of motion is:

T=2Ï€rvT = \frac{2\pi r}{v}

where TT is the period of motion, rr is the radius of the circular path, and vv is the speed of the ball.

Q: What is the unit of measurement for the period of motion?

A: The unit of measurement for the period of motion is time, typically measured in seconds (s).

Q: Can you provide a numerical example to illustrate the calculation of the period of motion?

A: Yes, let's consider an example where the radius of the circular path is 0.2 m0.2 \, \text{m} and the speed of the ball is 10 m/s10 \, \text{m/s}. Using the formula, we get:

T=2π×0.2 m10 m/s=1.257 m10 m/s=0.1257 sT = \frac{2\pi \times 0.2 \, \text{m}}{10 \, \text{m/s}} = \frac{1.257 \, \text{m}}{10 \, \text{m/s}} = 0.1257 \, \text{s}

Conclusion

In conclusion, the period of motion is an important concept in the study of circular motion. It helps us understand the time taken by an object to complete one full revolution around a circular path. We hope this Q&A article has provided you with a better understanding of the period of motion and its significance in real-life situations.

Additional Information

  • The period of motion is a measure of the time taken by an object to complete one full revolution around a circular path.
  • The period of motion is related to the speed of the object and the radius of the circular path by the equation T=2Ï€rvT = \frac{2\pi r}{v}.
  • The period of motion is an important concept in physics, particularly in the study of circular motion.

References

  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
  • Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.