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?
To find the moment of inertia of the wheel, you can use the formula:
Torque = Moment of Inertia x Angular Acceleration
Rearranging the formula, we get:
Moment of Inertia = Torque / Angular Acceleration
Plugging in the given values:
Moment of Inertia = 32 Nm / 25 rad/s^2
Calculating:
Moment of Inertia = 1.28 Nm/(rad/s^2)
So, your calculation of 1.28 kg/m^2 is incorrect. The correct unit for moment of inertia is kg.m^2.
To find the rotational moment of inertia of the wheel, we can use the formula:
τ = Iα
Where:
τ is the torque applied to the wheel (32 Nm)
I is the moment of inertia
α is the angular acceleration (25 rad/s^2)
Rearranging the formula, we have:
I = τ / α
Substituting the given values, we get:
I = 32 Nm / 25 rad/s^2
Calculating this equation gives us:
I = 1.28 kg⋅m^2
Hence, your answer of 1.28 kg⋅m^2 is correct.