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 an object, you need to know its mass and 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.
The moment of inertia (I) for a rotating object can be calculated using the formula:
I = m * r^2
where I is the moment of inertia, m is the mass of the object, and r is the radius of gyration.
Substituting the given values into the formula, we have:
I = 100 kg * (0.6 cm)^2
To calculate the moment of inertia, we need to convert the radius of gyration from centimeters (cm) to meters (m) since the standard SI unit for length is meters.
1 cm = 0.01 m
So, the radius of gyration in meters would be:
r = 0.6 cm * 0.01 m/cm = 0.006 m
Now, substituting the values into the formula again:
I = 100 kg * (0.006 m)^2
I = 0.036 kg * m^2
Thus, the moment of inertia of the airplane propeller is 0.036 kg * m^2.
To calculate the torque required to give the propeller an angular acceleration, we can use the formula:
T = I * α
where T is the torque, I is the moment of inertia, and α is the angular acceleration.
Substituting the given angular acceleration of 20 rad/sec^2 and the calculated moment of inertia of 0.036 kg * m^2 into the formula, we have:
T = 0.036 kg * m^2 * 20 rad/sec^2
T = 0.72 kg * m^2 * rad/sec^2
Therefore, the torque required to give the airplane propeller an angular acceleration of 20 rad/sec^2 is 0.72 kg * m^2 * rad/sec^2.