Question

if w= 2.5 rad/s , and r= 1.5m find v and centripetal acceleration?​

Answer 1

Answer:

• Angular velocity (ω) = 2.5 rad/s
• Radius (r) = 1.5 m
• linear velocity (v) = ?
• Centripetal Acceleration (a) = ?

Relation between Linear velocity and Angular velocity is given as :

$\longrightarrow\:\:\tt v = r\omega$

Substitue the known values in above formula :

$\longrightarrow\:\:\tt v = 1.5 \times 2.5$

$\longrightarrow\:\: \underline{ \underline{\tt v = 3.75 \: {ms}^{ - 1}}}$

Now, let's find the centripetal acceleration ;

Method 1 :-

$\longrightarrow\:\:\tt a_c= \dfrac{v^2}{r}$

$\longrightarrow\:\:\tt a_c= \dfrac{(3.75)^2}{1.5}$

$\longrightarrow\:\:\tt a_c= \dfrac{14.0625}{1.5}$

$\longrightarrow\:\: \underline{ \underline{\tt a_c= 9. 375 \: {ms}^{ - 2}}}$

Method 2 :-

$\longrightarrow\:\:\tt a_c= \omega^2 r$

$\longrightarrow\:\:\tt a_c= (2.5)^2 \times 1.5$

$\longrightarrow\:\:\tt a_c= 6.25 \times 1.5$

$\longrightarrow\:\: \underline{ \underline{\tt a_c= 9. 375 \: {ms}^{ - 2}}}$