Question

a 100cm rod is moving on a horizontal surface at an instant when it is parallel to the x-axis its ends A and B have velocities 20 cm per second and 30n cm per second as shown in the figure find the angular velocity of the rod​

Answer 1

Given that,

Radius = 100 cm

Velocity of A = 20 cm/s

Velocity of B = 30 cm/s

Angular velocity :

Angular velocity is equal to the linear velocity divided by radius.

In mathematically,

$\omega=\dfrac{v}{r}$

Where, v = linear velocity

r = radius  

Let the rod is rotating with uniform angular velocity and the center of rotation of the 100cm rod is r cm away from the end rotating with tangential velocity 20 m/s.

We need to calculate the radius

Using formula of angular velocity

For A,

$v=r\omega$

$20=\omega r$....(I)

For B,

$30=(100-r)\omega$......(II)

From equation (I) and (II)

$\dfrac{20}{30}=\dfrac{r}{100-r}$

$2000-20r=30r$

$r=\dfrac{2000}{50}$

$r= 40 cm$

We need to calculate the angular velocity

Put the value of r in equation (I)

$20=40\omega$

$\omega=\dfrac{20}{40}$

$\omega=0.5\ rad/s$

Hence, The angular velocity of the rod​ is 0.5 rad/s.