Question

if the angular velocity of a ball is 72km/h. Radius is 4 m . find torque and angular momentum​

Answer 1

Given that,

Angular velocity = 72 km/h

Radius = 4 m

Suppose the mass of ball is 20 kg and angular acceleration is 2 rad/s²

We need to calculate the angular velocity

Using formula of angular velocity

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

Put the value into the formula

$\omega=\dfrac{72\times\dfrac{5}{18}}{4}$

$\omega=5\ /sec$

We need to calculate the moment of inertia

Using formula of moment of inertia

$I=\dfrac{2}{5}mr^2$

Put the value into the formula

$I=\dfrac{2}{5}\times20\times4^2$

$I=128\ kgm^2$

We need to calculate the torque

Using formula of torque

$\tau=I\alpha$

$\tau=128\times2$  

$\tau=256\ N-m$

We need to calculate the angular momentum

Using formula of angular momentum

$L=I\omega$

Put the value into the formula

$L=128\times5$

$L=640\ kg m^2/s$

Hence, The torque is 256 kgm/s^2.

The angular momentum is 640 kg m^2/s.