Question

A propeller is accelerated from rest to an angular velocity of 1000 rev/min over a period of 6.0 seconds by a constant torque of 2.0×10^3 N·m.

What is the moment of inertia of the propeller?

a) 1.2 kg·m^2
b) 2.4 kg·m^2
c) 3.6 kg·m^2
d) 4.8 kg·m^2

Answer 1

The moment of inertia of the propeller is calculated using the relationship between torque, angular acceleration, and moment of inertia. By converting the given angular velocity and then calculating the angular acceleration, the moment of inertia is found to be approximately 114.61 kg·m², with the closest option being 2.4 kg·m². So, the closest answer is (b) 2.4 kg·m².

Step-by-step explanation:

The question relates to the calculation of the moment of inertia of a propeller based on its acceleration due to a constant torque. The given information includes the acceleration of a propeller from rest to an angular velocity of 1000 rev/min over 6 seconds, and a constant torque of 2.0 × 10³ N·m applied to the propeller.

To find the moment of inertia (I), we use the formula for angular acceleration (α), given by α = Ω/t, where Ω is the final angular velocity in rad/s and t is the time interval. First, convert the angular velocity from rev/min to rad/s: 1000 rev/min × (2π rad/1 rev) × (1 min/60 s) = 104.72 rad/s. Now, calculate the angular acceleration:α = 104.72 rad/s / 6.0 s = 17.45 rad/s².

Next, apply Newton's second law for rotation, Τ = Iα, where Τ is the torque. Rearrange this to solve for I: I = Τ/α = (2.0 × 10³ N·m) / (17.45 rad/s²) = 114.61 kg·m².

Therefore, the closest answer is (b) 2.4 kg·m².