Refer to (Figure) for the moments of inertia for the individual objects. In both cases, the moment of inertia of the rod is about an axis at one end. In (b), the center of mass of the sphere is located a distance R from the axis of rotation. In (a), the center of mass of the sphere is located at a distance L+R from the axis of rotation. Since we have a compound object in both cases, we can use the parallel-axis theorem to find the moment of inertia about each axis. 34-2Magnetic moments and angular momentum 34-3The precession of atomic magnets. The radius of the sphere is 20.0 cm and has mass 1.0 kg. the tensor of inertia 31-5The cross product 31-6The tensor of stress. The rod has length 0.5 m and mass 2.0 kg. Results, with a single weight (m 2 = 50 g), in a proportionality factor of 0.43 or with two weights (m 2 = 0.1 kg) of 0.86.Find the moment of inertia of the rod and solid sphere combination about the two axes as shown below. With the estimated moment of inertia (with the simplifying assumption of an homogeneous and point mass) The gradient of the straight line is the proportionality factorįor the example with one weight 0.45, with two weights 0.91. In the diagram of the dependency of the precession frequency f P on the rotational frequency f D a hyperbola is found, or, in the diagram of f P plotted against 1/f D a straight line, i.e. Moment of inertia of a thin rod about its centre We have a formula for the moment of inertia of a point mass, m, a distance r from the rotation axis: I m r2 To calculate the moment of inertia of an extended body, split it into an infinite number of point masses and add their moments of inertia together. Repeat the experiment with two suspended weights (100 g). If necessary, the gyroscope disk may be braked somewhat. Rotate the gyroscope back and start precession repeatedly for decreasing rotational frequencies and make measurements.
This allows us to find the period of precession. The precession of the gyroscope is best obtained by starting up the gyroscope without nutation. We use Equation 11.12 to find the precessional angular velocity of the gyroscope. The precession motion must not be overlaid by the nutation movement. 10 Hz.Īllow the gyroscope to precess and - once the gyroscope precesses uniformly - take a measurement by means of. The maximum rotational frequency is approx. Start the gyroscope disk rotating rapidly by means of a piece of string. 0.05 Hz) should be displayed after a short time. Rotate the gyroscope slowly about its vertical axis, the precession frequency (approx. Test of the correct adjustment of the rotary motion sensor If necessary, move the reflection light barrier slightly. (4ed) 10.4 A flywheel in the shape of a solid cylinder of radius R 0.60 m and mass M 15 kg can be brought to an angular speed of 12 rad/s in 0.60 s by a motor exerting a constant torque. Testing of the correct adjustment of the reflection light barrier Using energy methods, calculate the moment of inertia of the can if it takes 1.50 s to reach the bottom of the incline. This equation is exactly Equation 10.25 but with the torque and angular acceleration as vectors. The gyroscope should be precisely horizontally aligned above the adjustment screws on the foot. Identifying the first term on the left as the sum of the torques, and mr2 m r 2 as the moment of inertia, we arrive at Newton’s second law of rotation in vector form: net I.Then hang a weight (50 g) on the end of the gyroscope rod on the same side as the balancing mass.
To do this, the period T D of the rotational motion of the gyroscope disk is measured, and from this the rotational frequency f D = 1/T D is calculated. What is the precessional period of the gyroscope Strategy We use to find the precessional angular velocity of the gyroscope. The rotational frequency is determined by means of the reflection light barrier. Its center of mass is 5.0 cm from the pivot and the radius of the disk is 5.0 cm.
The precession frequency (frequency f B1) is measured directly using the rotary motion sensor. The moment of inertia of the gyroscope disk is given approximately by: d and the rotational frequency f D of the gyroscope disk.In the experiment, the precession frequency f P of a gyroscope is investigated as a function of the exerted force F, i.e. Open topic with navigation Precession of a gyroscopeĬan also be carried out with Mobile-CASSY 2 and Pocket-CASSY
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