An areoplane 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, we can use the formula:
I = m * k^2
where
I is the moment of inertia,
m is the mass of the object, and
k is the radius of gyration.
In this case, the mass of the airplane propeller is given as 100 kg and the radius of gyration is given as 0.6 cm (or 0.006 m). Plugging these values into the formula, we have:
I = 100 kg * (0.006 m)^2
I = 0.036 kg·m²
So, the moment of inertia of the airplane propeller is 0.036 kg·m².
To find the torque required to give it an angular acceleration of 20 rad/sec², we can use the formula:
τ = I * α
where
τ is the torque,
I is the moment of inertia, and
α is the angular acceleration.
Plugging in the values, we get:
τ = 0.036 kg·m² * 20 rad/sec²
τ = 0.72 N·m
Therefore, a torque of 0.72 N·m is required to give the airplane propeller an angular acceleration of 20 rad/sec².