Describing Motion Around Us · Lesson 9 of 10
Motion in a Plane
“Going in circles keeps speed steady while velocity changes its mind.”
• Distinguish one-dimensional motion from motion in a plane. • Compare distance and displacement along a circle. • Calculate average speed for one revolution. • Explain why average velocity is zero after a complete revolution. • Distinguish constant speed from constant velocity. • Explain acceleration in uniform circular motion. • Identify the tangent as the instantaneous velocity direction.
A car overtaking another does more than move forward; it also shifts sideways. A kicked ball changes both horizontal and vertical position. These motions cannot be represented completely on a single straight line. They take place in a plane.
Motion in a plane is motion that requires two dimensions to describe the changing position.
An overtaking vehicle, a kicked ball and a satellite seen in a circular path are examples. The chapter focuses on a particularly important two-dimensional case: motion around a circle.
Uniform circular motion
Circular motion is the motion of an object along a circular path.
When a child on a merry-go-round moves from one point to another, distance is the arc of the circle travelled, while displacement is the straight chord directed from the first point to the second. After a complete revolution, the distance is the circumference (2π R), but the final position equals the initial position, so displacement is zero.
Problem
A child moves on a circular path of radius 4 m and completes one revolution in 8 s. Find average speed and average velocity.
- 1.Distance in one revolution = (2π R=2π×4=8π m).
- 2.Average speed = (8π÷8=π m s⁻¹), approximately (3.14 m s⁻¹).
- 3.After one revolution, final and initial positions are the same.
- 4.Displacement = 0.
- 5.Average velocity = (0÷8=0 m s⁻¹).
Uniform circular motion is motion along a circular path at constant speed.
Constant speed does not mean constant velocity. Velocity includes direction. Along a rectangular track, direction changes at four corners; along a hexagonal track, it changes at six. As the number of sides increases, the path approaches a circle and the direction changes continuously.
Activity: Let us investigate
Place a marble inside a flat ring and send it around the inner boundary. Predict its motion when the ring is lifted. When the circular constraint disappears, the marble does not continue curving; it moves approximately along the straight direction it had at the instant of release.
Ready to Go Beyond
A tangent is a straight line that touches a circle at one point.
Instantaneous velocity in circular motion is directed along the tangent in the direction of motion. Although speed remains constant, this direction changes continuously. Since velocity changes, acceleration is non-zero. Circular motion therefore provides the clearest example of acceleration caused by direction change alone.
Problem
Explain the result of lifting the ring.
- 1.While touching the ring, the marble is continually redirected along the circular boundary.
- 2.At every instant, its velocity points along the tangent.
- 3.Lifting the ring removes the inward interaction that was changing the direction.
- 4.The marble continues approximately in its instantaneous tangential direction.
Note
Uniform circular motion is an idealised model because real objects rarely maintain a perfectly circular path and exactly constant speed. It remains useful for understanding planetary revolutions, rotating devices and vehicles negotiating circular turns.
Motion through space may require three dimensions, as with a bird flying or a vehicle following a winding mountain road. That extension is introduced only to show that one-dimensional and two-dimensional descriptions belong to a larger framework.
Velocity remains constant only when both magnitude and direction remain unchanged. In circular motion, direction changes at every point.
Quiz
Which description best matches Motion in a Plane?
Which description best matches Circular Motion?
Which term matches this description: Motion in a plane is motion that requires two dimensions to describe the changing position.
Which term matches this description: Circular motion is the motion of an object along a circular path.
Which statement is a key takeaway from this lesson?
Practice Problems
- A runner completes a circular track of radius 35 m in 44 s. Find average speed for one lap and average velocity.
- Compare distance and displacement after half a revolution.
- Explain why an object in uniform circular motion is accelerating.
- Draw velocity directions at the top, right, bottom and left points of a circle.
Key Takeaways
• Motion in a plane requires two dimensions. • Circular distance follows an arc; displacement follows a chord. • One complete revolution has distance (2π R) and zero displacement. • Uniform circular motion has constant speed but changing velocity. • Instantaneous velocity is tangential, so acceleration is present.