A torque of 32Nm is applied to a wheel, which causes it to accelerate at 25 rad/s2. What is the rotational moment of inertia of the wheel?
I got 1.28kg/m^2. Is this correct?
I= torque/angular accleration
= 32Nm/25rad/s^2=1.28 kg/m^2
cheers
To calculate the rotational moment of inertia of the wheel, we can use the formula:
τ = I * α
where τ is the torque applied to the wheel, I is the rotational moment of inertia, and α is the angular acceleration.
Rearranging the equation, we have:
I = τ / α
Substituting the values given:
I = 32 Nm / 25 rad/s^2
Calculating the result gives:
I ≈ 1.28 kg m^2
Therefore, your calculation of 1.28 kg/m^2 is correct.
To calculate the rotational moment of inertia of the wheel, you can use the equation:
τ = Iα
Where:
τ is the torque applied to the wheel (given as 32 Nm)
I is the rotational moment of inertia of the wheel (what we are trying to find)
α is the angular acceleration of the wheel (given as 25 rad/s^2)
Rearranging the equation, we have:
I = τ / α
Substituting the given values, we get:
I = 32 Nm / 25 rad/s^2
I = 1.28 kg⋅m^2
So, based on your calculation, the rotational moment of inertia of the wheel is indeed 1.28 kg⋅m^2. Well done! Your answer is correct.