Speed in uniform circular motion: Class 9 practice
An object moving in a circle at constant speed covers the circumference 2πr in one period T, so v = 2πr/T. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Circumference
The idea behind speed in uniform circular motion
An object moving in a circle at constant speed covers the circumference 2πr in one period T, so v = 2πr/T. Its speed is constant but its velocity keeps changing direction.
Step-by-step method
- Find the circumference 2πr.
- v = 2πr/T.
- Convert units if needed.
Worked example 1 (Basic)
An object moves in a circle of radius 25 m and takes 4 s per revolution. Find its speed.
- v = 2π × 25 / 4
- = 39.27 m/s
- Answer: 39.27 m/s
Worked example 2 (Standard)
An object moves in a circle of radius 35 m and takes 45 s per revolution. Find its speed.
- v = 2π × 35 / 45
- = 4.89 m/s
- Answer: 4.89 m/s
Worked example 3 (Challenge)
An object moves in a circle of radius 50 km and takes 40 min per revolution. Find its speed.
- v = 2π × 50000 / 2400
- = 130.9 m/s
- Answer: 130.9 m/s
Common mistakes and misconceptions
- Using the diameter as r
- Saying the velocity is constant
Practice questions
- (Basic) An object moves in a circle of radius 8 m and takes 16 s per revolution. Find its speed.
- (Basic) An object moves in a circle of radius 12 m and takes 46 s per revolution. Find its speed.
- (Standard) An object moves in a circle of radius 19 m and takes 13 s per revolution. Find its speed.
- (Standard) An object moves in a circle of radius 24 m and takes 27 s per revolution. Find its speed.
- (Challenge) An object moves in a circle of radius 5 km and takes 32 min per revolution. Find its speed.
- (Challenge) An object moves in a circle of radius 8 km and takes 50 min per revolution. Find its speed.
Answer key with full working
- Q1: v = 2π × 8 / 16 → = 3.14 m/s → Answer: 3.14 m/s
- Q2: v = 2π × 12 / 46 → = 1.64 m/s → Answer: 1.64 m/s
- Q3: v = 2π × 19 / 13 → = 9.18 m/s → Answer: 9.18 m/s
- Q4: v = 2π × 24 / 27 → = 5.59 m/s → Answer: 5.59 m/s
- Q5: v = 2π × 5000 / 1920 → = 16.36 m/s → Answer: 16.36 m/s
- Q6: v = 2π × 8000 / 3000 → = 16.76 m/s → Answer: 16.76 m/s
Syllabus note
This skill is listed under "Motion" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is speed in uniform circular motion in?
"Motion", Class 9 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.