Question

a particle executes 4 revolutions per second on a circular path of radius 0.25 meter. find centripetal acceleration of the particle​

Answer 1

Explanation:

Frequency of rotation

n

=

2

r

p

s

Angular velocity of the rotating particle

ω

=

2

π

n

=

4

π

rad/s

Radius of the circular path

r

=

25

cm.

So radial acceleration of the particle

a

radial

=

ω

2

r

=

(

4

π

)

2

⋅

25

=

400

π

2

c

m

s

−

2

=

4

π

2

≈

39.48

m

s

−

2

Answer 2

Given:

A particle executes 4 revolutions per second on a circular path of radius 0.25 meter.

To find:

Centripetal acceleration of the object.

Calculation:

Let speed of object be v ;

$\rm{ \therefore \: v = \dfrac{distance}{time} }$

$\rm{ = > \: v = \dfrac{4 \times 2\pi r}{t} }$

$\rm{ = > \: v = \dfrac{8\pi r}{t} }$

$\rm{ = > \: v = \dfrac{8\pi (0.25)}{1} }$

$\rm{ = > \: v = \dfrac{8\pi ( \frac{1}{4} )}{1} }$

$\rm{ = > \: v = 2\pi \: m {s}^{ - 1} }$

Now , centripetal acceleration will be:

$\rm{ \therefore \: a = \dfrac{ {v}^{2} }{r} }$

$\rm{ = > \: a = \dfrac{ {(2\pi)}^{2} }{0.25} }$

$\rm{ = > \: a = \dfrac{ 4 {\pi}^{2} }{( \frac{1}{4} )} }$

$\rm{ = > \: a = 16 {\pi}^{2} \: m {s}^{ - 2} }$

So, final answer is:

$\boxed{ \bf{ \: a = 16 {\pi}^{2} \: m {s}^{ - 2} }}$