Question

A particle makes 240 revolution per minute on a circular radius of 2m find: (1) it's period (2) it's angular velocity (3) it's linear velocity (4) it's acceleration

Answer 1

(1) The period 0.25 secs

(2) The angular velocity is 25.14 rad/s

(3) The linear velocity is 50.28 m/s

(4) The acceleration is
`1264 m/s^(2)`

Step-by-step explanation:

(1) Period is defined as the time taken for one revolution

∴
`Period = (Time )/(Number of revolutions )`

From the question, the particle makes 240 revolution per minute

That is, For 240 revolution, the time taken = 1 minute

Time = 1 minute = 60 secs

Number of revolutions = 240

∴
`Period =(60)/(240) \\`

Period = 0.25 secs

The period 0.25 secs

(2) The angular velocity, ω is given by

ω
`= (2\pi )/(T) \\`

where
`T` is the period

∴ω = 2 ×
`(22)/(7)` / 0.25 (take
`\pi = (22)/(7)`)

ω = 25.14 rad/s

The angular velocity is 25.14 rad/s

(3) The linear velocity, v is given by

v = ωr

Where v is the linear velocity

ω is the angular velocity

and r is the radius

From the question, r = 2m

From v = ωr

∴v = 25.14 × 2

v = 50.28 m/s

The linear velocity is 50.28 m/s

(4) The acceleration is given by

`a =` ω × v = ω(ωr) =ω²r

∴
`a = 25.14^(2)` ×
`2`

`a = 1264.04 m/s^(2) \\a = 1264 m/s^(2)`

The acceleration is
`1264 m/s^(2)`