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) x radius of gyration (k)^2
Given:
Mass (m) = 100 kg
Radius of gyration (k) = 0.6 cm
First, we need to convert the radius of gyration to meters:
0.6 cm = 0.6/100 = 0.006 m
Now we can calculate the moment of inertia:
I = 100 kg x (0.006 m)^2
I = 100 kg x 0.000036 m^2
I = 0.0036 kg*m^2
The moment of inertia of the airplane propeller is 0.0036 kg*m^2.
To calculate the torque required to give it an angular acceleration of 20 rad/sec^2, we can use the formula:
Torque (τ) = Moment of inertia (I) x Angular acceleration (α)
Given:
Moment of inertia (I) = 0.0036 kg*m^2
Angular acceleration (α) = 20 rad/sec^2
Now we can calculate the torque:
τ = 0.0036 kg*m^2 x 20 rad/sec^2
τ = 0.072 kg*m^2/sec^2
The torque required to give the airplane propeller an angular acceleration of 20 rad/sec^2 is 0.072 kg*m^2/sec^2.