What is the angular momentum (in kg*m*m/s) of a 880 g symmetrical rotating bar which is 2.70 m long and spinning at 185 rpm about the center of the bar?
To calculate the angular momentum, we'll need to know the moment of inertia and the angular velocity of the rotating bar. The moment of inertia of a symmetrical bar is given by the formula:
I = (1/12) * m * L^2
Where:
- I is the moment of inertia,
- m is the mass of the bar,
- L is the length of the bar.
In this case, the mass of the bar is 880 g, which is equivalent to 0.880 kg. The length of the bar is 2.70 m. Plugging these values into the formula, we can find the moment of inertia:
I = (1/12) * 0.880 kg * (2.70 m)^2
Now, let's find the angular velocity of the bar. The angular velocity is given in revolutions per minute (rpm), but we need it in radians per second (rad/s) for our calculation. We can convert rpm to rad/s by using the formula:
ω = (2π * n) / 60
Where:
- ω is the angular velocity in rad/s,
- n is the number of revolutions per minute.
In this case, the angular velocity is 185 rpm. Plugging this value into the formula, we can find the angular velocity:
ω = (2π * 185) / 60
Now that we have both the moment of inertia (I) and the angular velocity (ω), we can calculate the angular momentum (L) using the formula:
L = I * ω
Plugging the values into the formula, we get:
L = [(1/12) * 0.880 kg * (2.70 m)^2] * [(2π * 185) / 60]
Calculating this expression will give us the angular momentum of the rotating bar in kg*m^2/s.