Learning Objectives

• Understand the concept of motion in a circle
• Explore the relationship between angular velocity and centripetal force
• Learn to calculate key quantities in circular motion, such as angular displacement and velocity
• Investigate the relationship between linear and angular motion in rotating systems

Language Objectives

• Improve vocabulary related to physics, especially concepts like force, acceleration, and velocity
• Develop the ability to describe motion in both mathematical and qualitative terms
• Practice using the terminology correctly in context, including understanding and producing complex sentence structures

Glossary

• Centripetal Force — Центростремительная сила
• Angular Velocity — Угловая скорость
• Angular Acceleration — Угловое ускорение
• Circular Path — Круговая траектория
• Period — Период
• Frequency — Частота

Understanding Motion in a Circle

The motion of an object in a circle is influenced by various factors such as angular velocity, centripetal force, and the radius of the circle. The object experiences a constant acceleration towards the center of the circle, known as the centripetal force. This force is responsible for changing the direction of the object’s velocity, keeping it in a circular path.

The relationship between linear and angular motion can be described as follows: the linear velocity of an object moving in a circle is related to its angular velocity by the equation v = rω, where v is the linear velocity, r is the radius of the circle, and ω is the angular velocity. This equation links the rotational motion with the linear motion of the object.

In a circular motion, the object’s speed is constant, but its velocity is constantly changing due to the changing direction. This constant change in direction requires a force towards the center of the circle, which is provided by the centripetal force. As the object moves in a circle, the direction of the velocity changes but its magnitude stays the same, hence the acceleration is always directed towards the center.

Exercise: Term Memorization

Review the following terms and try to match them with their definitions:

• Centripetal Force — The force that acts on an object moving in a circle, directed towards the center of the circle.
• Angular Velocity — The rate of change of angular displacement with respect to time.
• Frequency — The number of complete rotations or oscillations per unit time.

Watch a Video on Circular Motion

Problem-Solving Examples

Let’s solve a problem step by step:

Problem: A car is moving in a circular track with a radius of 50 meters. If the car completes one lap in 10 seconds, calculate its angular velocity.

Step 1: We use the formula for angular velocity: ω = 2π / T
Step 2: Where T is the period (time for one complete revolution).
Step 3: Given that T = 10 seconds, we can calculate ω as follows:
ω = 2π / 10 = 0.628 radians/second.

Step 1: The formula for angular velocity is ω = 2π / T
Step 2: The time for one revolution is 10 seconds.
ω = 2π / 10 = 0.628 radians/second

Research Assignment: Explore the Simulation

Click on the link below to explore the simulation of circular motion and experiment with different variables:

Group Work Assignment

Work with a partner or group to create a presentation on the forces acting on an object in circular motion. Make sure to cover:

• Centripetal force
• Angular velocity
• Applications of circular motion in real life (e.g., amusement park rides, planetary motion)

Present your findings to the class.

Additional Resources

Explore the following resources to deepen your understanding of circular motion:

• Save My Exams — Circular Motion Resources

Reflection

After completing the exercises and watching the video, reflect on the following questions:

• What are the key differences between linear motion and circular motion?
• How does the concept of angular velocity help us understand rotational motion?
• How can we apply the knowledge of circular motion to real-life scenarios?