Chapter : 1. Motion
Examples on Circular Motion
Example : 16
A particle moves in a circle of radius 2 m and completes 5 revolutions in 10 seconds. Calculate the following :(i)
Angular velocity and
(ii) Linear velocity.
Solution. Since, it completes 5 revolutions in 10 seconds.
∴ Time period = 10/5 = 2s
(i) Now angular velocity,
= 2π / 2 = π rad/s
(ii) Linear velocity is given by
v = r ω = 2 π
∴ v = 2 π m/s
Example : 17
The length of second's needle in a watch is 1.2 cm. Calculate the following :
(i) Angular velocity and
(ii) Linear velocity of the tip of the needle.
Solution. (i)We know that the second's needle in a watch completes one revolution in 60 seconds.
∴ Time period, T = 60 s
Angular velocity,
(ii) Length of the needle = 1.2 cm = Radius of the circle
Linear velocity of the tip of the needle is given by
v = rω= 1.2 ×
or v = π/2s = 1.266 × 10–1 cm/sec.
Example : 18
Earth revolves around the sun in 365 days. Calculate its angular velocity.
Solution. Time period, T = 365 days = 365 × 24 × 60 × 60 seconds
∴ Angular Velocity, = 
rad/s = 1.99 × 10–7 rad/s.
A particle moves in a circle of radius 2 m and completes 5 revolutions in 10 seconds. Calculate the following :(i)
Angular velocity and
(ii) Linear velocity.
Solution. Since, it completes 5 revolutions in 10 seconds.
∴ Time period = 10/5 = 2s
(i) Now angular velocity,
= 2π / 2 = π rad/s(ii) Linear velocity is given by
v = r ω = 2 π
∴ v = 2 π m/s
Example : 17
The length of second's needle in a watch is 1.2 cm. Calculate the following :
(i) Angular velocity and
(ii) Linear velocity of the tip of the needle.
Solution. (i)We know that the second's needle in a watch completes one revolution in 60 seconds.
∴ Time period, T = 60 s
Angular velocity,
(ii) Length of the needle = 1.2 cm = Radius of the circle
Linear velocity of the tip of the needle is given by
v = rω= 1.2 ×
or v = π/2s = 1.266 × 10–1 cm/sec.
Example : 18
Earth revolves around the sun in 365 days. Calculate its angular velocity.
Solution. Time period, T = 365 days = 365 × 24 × 60 × 60 seconds
∴ Angular Velocity,
= rad/s = 1.99 × 10–7 rad/s.Trending Articles & Blogs
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