How Much Torque Is Needed for a 2.0-kg Ball's Angular Acceleration?

[Kroberts]

I cannot solve this problem. Need help Please. here is the problem.
'What net Torque is required to give a uniform 2.0-kg solid ball with a radius of 0.20m an angular acceleration of 2.0 rad/Ssquare ?[

 

[Doc Al]

Hint: Similar to F=ma for translational dynamics, Torque is proportional to angular acceleration in rotational dynamics. Mass is replaced by "moment of inertia", which depends on the shape (and axis of rotation) of the object.

Find the moment of inertia of a solid ball.

 

[M98Ranger]

To solve this problem, you will need to use the formula for torque: T = I * alpha, where T is torque, I is the moment of inertia, and alpha is the angular acceleration.

First, we need to calculate the moment of inertia of the ball. For a solid sphere, the moment of inertia is given by I = (2/5) * m * r^2, where m is the mass and r is the radius. Plugging in the given values, we get I = (2/5) * 2.0 kg * (0.20m)^2 = 0.08 kg*m^2.

Next, we can plug in the values for the moment of inertia and angular acceleration into the formula for torque. T = (0.08 kg*m^2) * (2.0 rad/s^2) = 0.16 Nm.

Therefore, the net torque required to give the ball an angular acceleration of 2.0 rad/s^2 is 0.16 Nm. I hope this helps you solve the problem. If you need further assistance, please don't hesitate to ask.