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

(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

Explanation:

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

∴

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 = 0.25 secs

The period 0.25 secs

(2) The angular velocity, ω is given by

ω

where is the period

∴ω = 2 × / 0.25           (take )

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

ω × v = ω(ωr) =ω²r

∴ ×

The acceleration is

we need to know the time interval during which the force acts. impulse of force = momentum change

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.