Question

A stone is tied to one end of a string and whirled in a horizontal circle of radius 1m at 20 revolution per minute. calculate the angular velocity and linear speed of the stone also find the centripetal acceleration​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• A stone tis tied to one end of the string in a horizontal Circle of Radius 1m .
• It makes 20 revolution in 1 min .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Find :- }}}}$

• The angular velocity .
• The linear speed .
• The centripetal acclⁿ .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution :- }}}}$

Given that the stone makes 20 revolution in 1min = 60s . Therefore the angular velocity will be 20/60 revolution / s = 1/3 revolution / s . Next we need to find out the linear speed . We know the relation between angular velocity , linear speed and radius as ,

$\sf\dashrightarrow Velocity = ( radius)* ( Angular \ velocity ) \\\\\\\sf\dashrightarrow v = r\omega \\\\\\\sf\dashrightarrow v = 1 \times \dfrac{1}{3} m/s \\\\\\\sf\dashrightarrow\underset{\blue{\sf Linear \ Speed }}{\underbrace{\boxed{\pink{\frak{ Speed ( v ) = 0.33 \ m/s }}}}}$

$\rule{200}2$

Finally we need to find out the Centripetal acceleration . We know that centripetal acceleration is v²/r . So that ,

$\sf\dashrightarrow Accl^n _{c}= \dfrac{ (velocity)^2}{Radius} \\\\\\\sf\dashrightarrow Accl^n_c = \dfrac{ (0.33 m/s)^2 }{1m } \\\\\\\sf\dashrightarrow\underset{\blue{\sf Centripetal\ Acceleration }}{\underbrace{\boxed{\pink{\frak{ \ Acceleration_{(centripetal)}= 0.11 \ m/s^2 }}}}}$

$\rule{200}2$

Answer 2

Answer:

acceleration =0.11 m/ s2

Explanation:

given:

a stone is tied to one end of the string in a horizontal circle of radius 1m

to find :

• the angular velocity
• the linear speed
• the centripetal acceleration

solution:

given that the stone marks 20

revolution in 1min =60 sec

•: the angular velocity 1s next we need to find out the linear speed , we known the relation between angular velocity, linear speed and radius as

= velocity =(radius) * (angular velocity)

v= rw

v = 1× 1/3 m/s

finally we need to find out the centripetal acceleration we know that centripetal acceleration is v2 / r , so that

A = ( velocity ) square/ radius

A=( 0.33m/s) square / 1m

A = 0.11m/ s square