Материал: Андрианова English Thesaurus of Student-Physicist 2013

Exercises

1. Rearrange the letters in the anagrams to form equivalents for the Russian words:

2. Match the words in A with the words in B to form word combinations:

3. Fill in the gaps with the missing words from the list:

circular motion, angular displacement, centripetal acceleration, instantaneous angular speed, gravitational constant

1.Each point on the disc undergoes the same _____ in any given time interval.

2.For very short time intervals, the average angular speed approaches the _____, just as in the linear case.

3.For _____ at constant speed, the acceleration vector always points toward the center of the circle.

4._____ itself is always directed towards the center of rotation.

5.The _____ was first measured in an important experiment by Henry Cavendish in 1798.

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UNIT 8

ROTATIONAL EQUILIBRIUM

AND ROTATIONAL DYNAMICS

Read the following texts. Study the thesaurus on fig. 8, answer the questions after the texts

In the study of linear motion, objects were treated as point particles without structure. It didn't matter where a force was applied, only whether it was applied or not.

The reality is that the point of application of a force does matter. In football, for example, if the ball carrier is tackled near his midriff, he might carry the tackier several yards before falling. If tackled well below the waistline, however, his center of mass rotates toward the ground, and he can be brought down immediately. Tennis provides another good example. A tennis ball is struck with a strong horizontal force acting through its center of mass, it may travel a long distance before hitting the ground, far out of bounds. Instead, the same force applied in an upward, glancing stroke will impart topspin to the ball, which can cause it to land in the opponent's court.

The concepts of rotational equilibrium and rotational dynamics are also important in other disciplines. For example, students of architecture benefit from understanding the forces that act on buildings and biology students should understand the forces at work in muscles and on bones and joints. These forces create torques, which tell us how the forces affect an object's equilibrium and rate of rotation.

Finally, torques applied to an object through a given time interval can change the object's angular momentum. In the absence of external torques, angular momentum is conserved, a property that explains some of the mysterious and formidable properties of pulsars - remnants of supernova explosions that rotate at equatorial speeds approaching that of light.

Torque

Forces cause accelerations; torques cause angular accelerations. There is a definite relationship, however, between the two concepts. If a force F is applied to the door, there are three factors that determine the effectiveness of the force in opening the door: the magnitude of the force, the position of application of the force, and the angle at which it is applied.

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Under these conditions, an object can rotate around the chosen axis in one of two directions. By convention, counterclockwise is taken to be the positive direction, clockwise the negative direction. When an applied force causes an object to rotate counterclockwise, the torque on the object is positive. When the force causes the object to rotate clockwise, the torque on the object is negative. If the net torque isn't zero, the object starts rotating at an ever-increasing rate. If the net torque is zero, the object's rate of rotation doesn't change.

Torque is a vector perpendicular to the plane determined by the position and force vectors. The direction can be determined by the right-hand rule.

An object in mechanical equilibrium must satisfy the following two conditions:

1.The net external force must be zero.

2.The net external torque must be zero.

The center of gravity

The center of mass and center of gravity of an object are exactly the same when the free-fall acceleration doesn't vary significantly over the object.

The center of gravity of a homogeneous, symmetric body must lie on the axis of symmetry. For example, the center of gravity of a homogeneous rod lies midway between the ends of the rod, and the center of gravity of a homogeneous sphere or a homogeneous cube lies at the geometric center of the object. The center of gravity of an irregularly shaped object, such as a wrench, can be determined experimentally by suspending the wrench from two different arbitrary points.

A rigid object in a uniform gravitational field can be balanced by a single force equal in magnitude to the weight of the object, as long as the force is directed upward through the object's center of gravity.

Relationship between torque and angular acceleration

When a rigid object is subject to a net torque, it undergoes an angular acceleration that is directly proportional to the net torque. This result is analogous to Newton's second law. The torque on the object is proportional to the angular acceleration of the object, where the constant of proportionality is called the moment of inertia of the object.

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Angular momentum

The net torque acting on an object is equal to the time rate of change of the object's angular momentum. Recall that this equation also parallels the impulse-momentum theorem.

The mechanical energy, linear momentum, and angular momentum of an isolated system all remain constant. If the moment of inertia of an isolated rotating system changes, the system's angular speed will change. Note that conservation of angular momentum applies to macroscopic objects such as planets and people, as well as to atoms and molecules.

There are many examples of conservation of angular momentum; one of the most dramatic is that of a figure skater spinning in the finale of her act. Coming out of the spin, she needs to reduce her angular velocity, so she extends her arms and legs again, increasing her moment of inertia and thereby slowing her rotation.

1.The point of application of a force does matter. Give examples.

2.What do torques cause?

3.What two conditions are necessary for an object in mechanical equilibrium?

4.What can you say about center of gravity of an object?

5.What result is a like Newton’s law?

6.What values of isolated system are always constant?

Exercises

1. Rearrange the letters in the anagrams to form equivalents for the Russian words:

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