A 2.0-m measuring stick of mass 0.215 kg is resting on a table. A mass of 0.500 kg is attached to the stick at a distance of 72.0 cm from the centre. Both the stick and the table surface are frictionless. The stick rotates with an angular speed of 6.50 rad/s.
(a) If the stick is pivoted about an axis perpendicular to the table and passing through its centre, what is the angular momentum of the system? ANS: 2.15
(b) If the stick is pivoted about an axis perpendicular to it and at the end that is furthest from the attached mass, and it rotates with the same angular speed as before, what is the angular momentum of the system?
ANS:?
I did a), but don't now how to do b). Also, b) equal 11 something, but cant seem to find the decimals.
Please help asap!
To find the angular momentum of the system in scenario (b), where the stick is pivoted about an axis perpendicular to it and at the end furthest from the attached mass, we need to consider the moment of inertia of the system.
In this scenario, the moment of inertia of the system will be different than in scenario (a), where the stick is pivoted through its center. The moment of inertia depends on the distribution of mass around the axis of rotation.
To calculate the moment of inertia of the system, we can use the parallel axis theorem. The parallel axis theorem states that the moment of inertia of an object about an axis parallel to and a distance "d" away from an axis through its center of mass is equal to the sum of the moment of inertia about the center of mass and the product of the object's mass and the square of the distance "d".
In this case, the moment of inertia of the stick about an axis through its center of mass is given by:
I_stick = (1/12) * m_stick * L^2
Where:
m_stick = mass of the stick
L = length of the stick
The moment of inertia of the mass attached to the stick is given by:
I_mass = m_mass * (r^2)
Where:
m_mass = mass of the attached mass
r = distance from the axis of rotation to the attached mass (in this case, it is the length of the stick, L)
So, the moment of inertia of the system, when pivoted about an axis at the end furthest from the attached mass, is given by:
I_system = I_stick + I_mass
Now we can calculate the angular momentum of the system using the formula:
L = I_system * ω
Where:
ω = angular speed (given as 6.50 rad/s)
Given the values in the problem statement, you can substitute them into the equations to find the angular momentum of the system in scenario (b).
Once you have calculated the angular momentum, you can round the result to the appropriate number of decimal places to match the answer given in the problem (if necessary).
I hope this explanation helps you solve the problem.