What net torque is required to give a uniform 12-kg solid ball with a radius of 0.22m an angular acceleration of 12rad/s2 ?
τ=Iε=(2mR²/5)ε=
=2•12•0.22²•12/5 =2.79 N•m
To find the net torque required to give a uniform solid ball an angular acceleration, we can use the equation:
τ = Iα
Where:
- τ represents the net torque
- I is the moment of inertia of the ball
- α is the angular acceleration
To find the moment of inertia, we need to use the formula for a solid sphere:
I = (2/5) * m * r^2
Where:
- m is the mass of the sphere
- r is the radius of the sphere
Given:
- Mass, m = 12 kg
- Radius, r = 0.22 m
- Angular acceleration, α = 12 rad/s^2
Let's solve it step by step:
1. Calculate the moment of inertia using the formula:
I = (2/5) * m * r^2
I = (2/5) * 12 kg * (0.22 m)^2
= (2/5) * 12 kg * 0.0484 m^2
≈ 0.195 kg * m^2
2. Substitute the moment of inertia and the given angular acceleration into the equation τ = Iα:
τ = I * α
τ = 0.195 kg * m^2 * 12 rad/s^2
≈ 2.34 N·m
Therefore, the net torque required to give the solid ball an angular acceleration of 12 rad/s^2 is approximately 2.34 N·m.