A mass of 1.0 kg is located at the end of a very light and rigid rod 44 cm in length. The rod is rotating about an axis at its opposite end with a rotational velocity of 3 rad/s.
(a) What is the rotational inertia of the system?
kg · m2
(b) What is the angular momentum of the system?
kg · m2/s
(a) I = M L^2
(b) I w
where w = 3 rad/s
To find the rotational inertia of the system, you need to use the formula for the rotational inertia of a point mass rotating about an axis:
I = m * r^2
Where:
I is the rotational inertia
m is the mass of the object
r is the distance between the axis of rotation and the mass
In this case, we know that the mass (m) is 1.0 kg and the distance (r) is 44 cm, which is equivalent to 0.44 m.
So, using the formula:
I = 1.0 kg * (0.44 m)^2
I = 0.1936 kg·m^2
Therefore, the rotational inertia of the system is 0.1936 kg·m^2.
To find the angular momentum of the system, you can use the formula for angular momentum:
L = I * ω
Where:
L is the angular momentum
I is the rotational inertia
ω (omega) is the angular velocity
In this case, we know that the rotational inertia (I) is 0.1936 kg·m^2 and the angular velocity (ω) is 3 rad/s.
Using the formula:
L = 0.1936 kg·m^2 * 3 rad/s
L = 0.5808 kg·m^2/s
Therefore, the angular momentum of the system is 0.5808 kg·m^2/s.