A solid cylinder of mass 2.0kg and radius 0.40cm being rotated about an axis through its Centre and parallel to its length with a frequency of 25Hz.Determine the angular momentum
angular momentum = Inertia*angularspeed
= ..5*m*r^2(2PI*25) you know m, r, calculate.
To determine the angular momentum of the solid cylinder, we need to use the equation:
Angular momentum (L) = moment of inertia (I) * angular velocity (ω)
First, let's find the moment of inertia of the solid cylinder. The moment of inertia of a solid cylinder rotating around its central axis is given by the formula:
I = 0.5 * m * r^2
Where:
m is the mass of the cylinder
r is the radius of the cylinder
In this case, the mass of the cylinder (m) is given as 2.0 kg, and the radius (r) is given as 0.40 cm. However, it is important to convert the radius to meters before plugging it into the formula. 1 cm = 0.01 m.
So, r = 0.40 cm = 0.40 * 0.01 = 0.004 m
Now we can calculate the moment of inertia (I):
I = 0.5 * 2.0 kg * (0.004 m)^2
I = 0.5 * 2.0 kg * 0.000016 m^2
I = 0.000016 kg*m^2
Next, we need to find the angular velocity (ω) in radians per second. The frequency (f) of rotation is given as 25 Hz. Angular velocity (ω) is related to frequency (f) by the equation:
ω = 2πf
Where:
π (Pi) is a mathematical constant approximately equal to 3.14159
Let's calculate the angular velocity (ω):
ω = 2π * 25 Hz
ω = 50π rad/s
ω ≈ 157.08 rad/s
Finally, we can calculate the angular momentum (L):
L = I * ω
L = 0.000016 kg*m^2 * 157.08 rad/s
L ≈ 0.0025 kg*m^2/s
Therefore, the angular momentum of the solid cylinder is approximately 0.0025 kg*m^2/s.