To study gyroscope and the angular moment.

                                                EXPERIMENT NO 10

Objective:

The object of the experiment is to study gyroscope and the angular moment.

Apparatus:

The TM  630 Gyroscope Apparatus.

           

Theory:

A gyroscope (from Ancient Greek γῦρος gûros, "circle" and σκοπέω skopéō, "to look") is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum. Because of this, gyroscopes are useful for measuring or maintaining orientation.

A gyroscope is a wheel mounted in two or three gimbals, which are a pivoted supports that allow the rotation of the wheel about a single axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow a wheel mounted on the innermost gimbal to have an orientation remaining independent of the orientation, in space, of its support. In the case of a gyroscope with two gimbals, the outer gimbal, which is the gyroscope frame, is mounted so as to pivot about an axis in its own plane determined by the support. This outer gimbal possesses one degree of rotational freedom and its axis possesses none. The inner gimbal is mounted in the gyroscope frame (outer gimbal) so as to pivot about an axis in its own plane that is always perpendicular to the pivotal axis of the gyroscope frame (outer gimbal). This inner gimbal has two degrees of rotational freedom.

The axle of the spinning wheel defines the spin axis. The rotor is constrained to spin about an axis, which is always perpendicular to the axis of the inner gimbal. So the rotor possesses three degrees of rotational freedom and its axis possesses two. The wheel responds to a force applied to the input axis by a reaction force to the output axis.

The behavior of a gyroscope can be most easily appreciated by consideration of the front wheel of a bicycle. If the wheel is leaned away from the vertical so that the top of the wheel moves to the left, the forward rim of the wheel also turns to the left. In other words, rotation on one axis of the turning wheel produces rotation of the third axis.

A gyroscope flywheel will roll or resist about the output axis depending upon whether the output gimbals are of a free or fixed configuration. Examples of some free-output-gimbal devices would be the attitude reference gyroscopes used to sense or measure the pitch, roll and yaw attitude angles in a spacecraft or aircraft.

The centre of gravity of the rotor can be in a fixed position. The rotor simultaneously spins about one axis and is capable of oscillating about the two other axes, and, thus, except for its inherent resistance due to rotor spin, it is free to turn in any direction about the fixed point. Some gyroscopes have mechanical equivalents substituted for one or more of the elements. For example, the spinning rotor may be suspended in a fluid, instead of being pivotally mounted in gimbals. A control moment gyroscope (CMG) is an example of a fixed-output-gimbal device that is used on spacecraft to hold or maintain a desired attitude angle or pointing direction using the gyroscopic resistance force.

In some special cases, the outer gimbal (or its equivalent) may be omitted so that the rotor has only two degrees of freedom. In other cases, the centre of gravity of the rotor may be offset from the axis of oscillation, and, thus, the centre of gravity of the rotor and the centre of suspension of the rotor may not coincide.

Experimental Verification of Gyroscopic Laws:

In the experiment, the slider weight is set to various radii (r=25,50, 75,95 mm). the mass of the slider weight (m=65.6), the acceleration due to gravity, and the radius r of the slider weight produce the moment M_w dictated by the balance bar:

M_w =m.g.r = 0.0656 kg . 9.81 m/s² .r = 0.6435 N. r

This moment M_w is counteracted by the gyroscopic moment, causing the balance bae to be lifted to the horizontal position.

The theoretical gyroscopic moment M_k is calculated from the rotational speed of the frame n_f , the rotational speed of the gyro n_e and  the mass moment of inertia of the gyro J_z (J_{z =} 375cm²g) as follows:

M_k= ω_f  ω_e J_z = 2л/60.n_f . 2л/60 n_e . 0.0000375 kg/m²

Procedure:

·         Place the protective hood in the retaining ring.

·         Turn the two speed potentiometers to zero.

·         Switch on the motor for the gyro.

·         With the speed potentiometer run upto the desired rotational speed.

·         Switch on the motor for the frame (gyroscope).

·         With speed potentiometer increase the rotational speed until the balance bar is horizontally aligned.

·         Make a note on both rotational speed.

Data and Observations:

Radius r (m)	Moment Mw (Nm)	Rotational speed ne (rpm)	Rotational speed nf (rpm)	Moment Mk (Nm)	Derivation (%)

Graphical Representation:

Conclusion:

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