Final answer:
Torque required by a motor can be calculated using the relationship between torque, angular acceleration, and moment of inertia. By converting the final angular speed to rad/s and knowing the time frame, one can find the angular acceleration. Multiplying this by the moment of inertia, if provided, would give the needed torque.
Step-by-step explanation:
To calculate the torque that must be supplied by the motor to take the disk from 0 to 2000 rpm in 4.1 seconds, we can use the relationship between torque, angular acceleration, and moment of inertia. First, we convert the final angular velocity from rpm to rad/s:
2000 rpm * (2π rad/rev) * (1 min/60 s) = 209.44 rad/s
Now, we find the angular acceleration (α) using the formula:
α = (ω_f - ω_i) / δt
where ω_f is the final angular velocity, ω_i is the initial angular velocity (0 rad/s since it starts from rest), and δt is the time interval. Substituting the values we have:
α = (209.44 rad/s - 0 rad/s) / 4.1 s
α = 51.08 rad/s²
Using the formula for torque (τ) which is related to moment of inertia (I) and angular acceleration (α):
τ = I * α
Without the moment of inertia provided, we cannot calculate the exact torque. However, if you have the moment of inertia of the disk, you can multiply it by the angular acceleration we found earlier to get the torque required.