1. Circular Motion
Standard 9

2. Distance travelled = 2πr
Circular Motion
Object moves around a circular path.
If the speed remains constant then it is called as uniform circular motion.
Such a body is always accelerating because there is a constant change in the direction of motion.
e.g. motion of earth around the sun
Distance travelled = 2πr
Speed = Distance / Time

3. Circular Motion - Equationsvt
Radius = r m
Distance travelled in one rotation = 2Π𝑟 m
Time for one rotation = T s
Speed (v) = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆 = 𝟐𝜫𝒓 𝑻 𝒎/𝒔
In a small time interval t, the object covers 𝑣𝑡 m.
By Pythagoras theorem –
(𝑟+𝑥) 2 = 𝑟 2 + (𝑣𝑡) 2
∴ 𝑟 2 +2𝑟𝑥+ 𝑥 2 = 𝑟 2 + (𝑣𝑡) 2
Since x is very small, 𝑥 2 is even smaller.
∴ 2𝑟𝑥 = (𝑣𝑡) 2
∴ 𝑥 = 1 2𝑟 (𝑣𝑡) 2
Comparing with 2nd equation of motion 𝑠=𝑢𝑡 𝑎 𝑡 2 𝑚
𝐚= 𝒗 𝟐 𝒓 𝐦/ 𝒔 𝟐 x
Radius = r r