An aeroplane propeller has a 100kg and radius of gyration of 0.6cm.find its moment of inertia.How large a torque is required to give it angular acceleration of 20rad/sec^2
To find the moment of inertia of the airplane propeller, we can use the formula:
Moment of Inertia (I) = mass (m) × radius of gyration (k)²
Given:
Mass (m) = 100 kg
Radius of Gyration (k) = 0.6 cm = 0.006 m
Plugging the values into the formula:
I = 100 kg × (0.006 m)²
I = 100 kg × 0.000036 m²
I = 0.0036 kg.m²
So, the moment of inertia of the airplane propeller is 0.0036 kg.m².
To find the torque required to give it an angular acceleration, we can use the formula:
Torque (τ) = moment of inertia (I) × angular acceleration (α)
Given:
Moment of inertia (I) = 0.0036 kg.m²
Angular acceleration (α) = 20 rad/sec²
Plugging the values into the formula:
τ = 0.0036 kg.m² × 20 rad/sec²
τ = 0.072 N.m
Therefore, the torque required to give the airplane propeller an angular acceleration of 20 rad/sec² is 0.072 N.m.