A certain wheel has a rotational inertia of 12 kg m^2. As it turns though 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant its value is:
To determine the torque exerted on the wheel, we can use the law of rotational motion, which states that torque (τ) is equal to the product of rotational inertia (I) and angular acceleration (α), i.e., τ = I * α.
In this case, we are given the rotational inertia of the wheel, which is 12 kg m^2, and the change in angular velocity (from 5.0 rad/s to 6.0 rad/s) when it completes 5.0 revolutions.
First, let's convert the 5.0 revolutions to radians by multiplying it by 2π (since 1 revolution = 2π radians):
5.0 revolutions * 2π radians/revolution = 10π radians
Next, we'll find the change in angular velocity (Δω):
Δω = 6.0 rad/s - 5.0 rad/s = 1.0 rad/s
Now, we can calculate the angular acceleration (α) using the formula Δω = α * Δt, where Δt is the change in time (which is not given in this case). However, since the net torque is constant, we can assume a constant angular acceleration for simplicity.
Let's assume Δt = 1 second (the actual value of Δt doesn't matter since we assume constant acceleration):
Δω = α * Δt → 1.0 rad/s = α * 1 s → α = 1.0 rad/s^2
Now, we can find the torque (τ) using the formula: τ = I * α
τ = 12 kg m^2 * 1.0 rad/s^2 = 12 N·m
Therefore, the value of the net torque exerted on the wheel is 12 N·m.