Example 1 · level 1
A car takes a circular turn of radius 50 m at a steady 20 m/s. Find its centripetal acceleration (in m/s², correct to 2 decimal places).
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- a = 400 ÷ 50 = 8 m/s².
Answer: 8
CLASS 11–12 PHYSICS · MOTION IN A PLANE / LAWS OF MOTION
Uniform circular motion
Centripetal acceleration a = v²/r = ω²r, force F = mv²/r. On a flat curve, friction provides it: v_max = √(μrg).
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Worked examples
Example 2 · level 2
A 0.1 kg stone tied to a string is whirled in a horizontal circle of radius 0.5 m, making one revolution every 1 s. Find the tension (centripetal force) in the string (in N, correct to 2 decimal places). Ignore gravity's effect on the string.
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- ω = 2π/1 = 6.28 rad/s.
- F = 0.1 × 6.28² × 0.5 = 1.97 N.
Answer: 1.97 N
Example 3 · level 3
On a flat (unbanked) curve of radius 40 m on a ghat road, the coefficient of static friction between tyres and road is 0.2. Find the maximum safe speed (in m/s, correct to 2 decimal places). Take g = 10 m/s².
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- v_max = √(80) = 8.94 m/s (= 32.18 km/h).
Answer: 8.94