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š¬ Same speed, still accelerating?
On a merry-go-round the speed can stay constant, yet the motion is accelerated. How can that be?
What is uniform circular motion, and its distance and displacement?
- When an object moves in a circular path, its motion is circular motion . If the speed is constant, it is uniform circular motion .
- In one revolution of a circle of radius \(R\): distance travelled \(= 2\pi R\) (the circumference), but displacement \(= 0\) (it returns to the start).
- If one revolution takes time \(T\): $$v_{av} = \dfrac{2\pi R}{T} \quad \text{(4.5)}$$ while the average velocity over one revolution is 0.
Why is uniform circular motion accelerated?
- Velocity changes if its magnitude or its direction (or both) changes.
- In uniform circular motion the speed is constant, but the direction of velocity changes continuously — so the motion is accelerated .
- The velocity at any point is along the tangent to the circle at that point, in the direction of motion.
Important Definitions
- Circular motion — the motion of an object moving along a circular path.
- Uniform circular motion — motion of an object in a circular path with constant (uniform) speed; it is accelerated because the direction of velocity keeps changing.
- Tangent — a straight line that meets the circle at one and only one point; the velocity at a point is along the tangent at that point, in the direction of motion.
š¹ Ready to Go Beyond — tangent to a circle
- The velocity at a point is along the tangent to the circle at that point, in the direction of motion.
- A tangent is a straight line that meets the circle at one and only one point. You will learn more about it in Mathematics.
In this Activity, we will spin a marble inside a ring and then lift the ring to discover the direction in which the freed marble moves.
Steps
- Place a ring (e.g. an adhesive-tape ring) flat on a smooth surface and roll a marble so it goes around the inner boundary.
- After a revolution or two, lift the ring without disturbing the marble. What path does the marble now take?
- Repeat a few times to confirm.
What you observe
- Once released, the marble moves in a straight line — along the direction (tangent) it had at the instant the ring was removed. You will learn the reason in a later chapter.
ā Note
- In uniform circular motion the speed is constant at every point; only the direction of velocity changes .
- Uniform circular motion is an idealised model, yet a useful one — it underlies planets orbiting the Sun and a vehicle making a circular turn.
ā Note
- In everyday life we call a vehicle ‘accelerating’ only when its speed changes, but a change in the direction of velocity is acceleration too — something we often fail to recognise.
NCERT Question 3 — A girl is riding her
Her speedometer reading is constant. Can the scooter still be accelerating, and if so, how?
View the answer →NCERT Question 16 — Rohan studies science from 6
For the minute hand (length 7 cm) between 6:00 and 7:30 PM, find its distance, displacement, speed and velocity.
View the answer →
š¹ Ready to Go Beyond — motion in three dimensions
- Motion in space — a car climbing up a mountain road, a bird flying in the sky, or an aircraft moving through air — is called motion in three dimensions . You will learn about it in higher grades.
Concept Map
Motion
A change of position with time, judged from a reference point.
Straight-line motion
Position, distance and displacement along a line.
Speed, velocity, acceleration
Averages and rates of change of position and velocity.
Kinematic equations
v=u+at, s=ut+½at², v²=u²+2as (constant a).
Motion graphs
A visual picture of how motion changes with time.
Position-time & velocity-time
Slope and area give velocity, acceleration and displacement.
Motion in a plane
Two-dimensional motion such as circular paths.
Uniform circular motion
Constant speed but continuously changing direction, so accelerated.
