Download Physics 2048 Lab 7

Physics 2048 Lab 7
Rotational Motion and Moment of Inertia
Introduction: In this lab you will study the rotational motion and moment of inertia of a rotating
disk using the concept of conservation of energy. You will determine the moment of inertia of
the disk by applying an angular acceleration
Theory: In the case of linear motion, an unbalanced force F acting on an object gives it an
acceleration a by Newton’s second law. After some time the object will be moving with some
velocity v and have an associated translational kinetic energy. The equations
of force and translational kinetic energy both depend on the mass, m, of the object and are given
by
F = ma
Ktr = ½ mv2
In the case of rotational motion, an unbalanced torque acting on an object causes it to rotate
with an angular acceleration . After some time the object will be rotating with some angular
velocity and have an associated rotational kinetic energy. The equations for torque and
rotational kinetic energy both depend on the moment of inertia, I, of the object and are given by
= IKrot = ½ I2
As mentioned above, an unbalanced force F applied any distance from a body’s center of mass
produces an unbalanced torque , the magnitude of which is given by
= rF
where r is the radius of the disc. You will use this principal to produce a rotational acceleration
in a disc by rotating it on an incline. By allowing the disc to fall, it will lose its gravitational
potential energy as it falls. Thus, the gravitational potential energy is converted to translational
kinetic energy and rotational kinetic energy of the disc. Applying the concept of conservation of
energy we have
Ugi + Ktri + Kroti = Ugf + Ktrf + Krotf
In this case the initial kinetic energies and the final potential energy will be zero, giving
Ugi = Ktrf + Krotf
mgh = ½ mvf 2 + ½ If 2
Equipments
Solid disc, hollow disc lab jack, timer and meter stick
Experimental Procedure
1- Make an incline using the table and the lab Jack.
2- Measure the mass of the disc and its initial height above the floor then calculate the initial
potential energy.
3- Then, by timing the fall of the rotating disc to the end of the table and by measuring the
distance then the final velocity can be calculated,
4- Allowing the final kinetic energy to be determined. Finally, the linear velocity can be
related to the angular velocity of the disc. = r , where  is the angular velocity, r is the
radius of the disc and  is the linear velocity
5- Calculate the moment of inertia of the disc, I, form the conservation of energy equation.
6- Repeat steps 2-5 about 6 times and get the average moment of inertia.
7- Repeat steps 2-6 using a different disc and again determine the average moment of inertia
for the disc.
8- Calculate the percent difference between the average moment of inertia