A wheel initially rotating at 12 rad/s decelerates uniformly to rest in 0.4 s. If the wheel has a rotational inertia of 0.5 kg. m², what is the magnitude of the torque causing this deceleration? (A) 1.5 N. m (B) 15 N. m (C) 30 Nm (D) 38 Nm​

(B) 15 N.m

Explanation:

The deceleration of the wheel is first found by using the following formula:

where,

α = angular acceleration = ?

ωf = final angular speed = 0 rad/s

ωi = initial angular speed = 12 rad/s

t = time = 0.4 s

Therefore,

here, the negative sign shows deceleration.

Now, we find the torque responsible for this deceleration:

where,

τ = torque = ?

I = rotational inertia = 0.5 kg.m²

Therefore,

τ = 15 N.m

Therefore, the correct answer is:

(B) 15 N.m

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