What constant torque,in the absence of friction,must be applied to a wheel to give it an angular velocity of 50 rad/s if it starts from rest and is accelerated for 10 s? The moment of inertia of the wheel about its axle is 9.0 kg · m². A)4.5 N · m B)9.0 N · m C)45 N · m D)30 N · m E)60 N · m

Question

Quizplus · Accepted Answer

We can use the formula for angular acceleration:

α = ωf - ωi / t

Where, 
α = Angular acceleration 
ωf= Final angular velocity = 50 rad/s (given) 
ωi= Initial angular velocity = 0 (given) 
t = Time taken = 10 s (given)

Substituting the values, we get:

α = (50-0) / 10 = 5 rad/s²

Now, we can use the formula for torque:

τ = Iα

Where, 
τ = Torque 
I = Moment of inertia = 9.0 kg · m² (given) 
α = Angular acceleration = 5 rad/s² (calculated)

Substituting the values, we get:

τ = 9.0 kg · m² * 5 rad/s² = 45 N · m

Therefore, the constant torque required to give the wheel an angular velocity of 50 rad/s is 45 N · m. 
Hence, the answer is C.

What Constant Torque,in the Absence of Friction,must Be Applied to a Wheel