1. what is the difference between rotational and translational equilibrium

Only the component that is perpendicular to the lever arm, or moment arm, causes a torque. In the image below, the vertical component F sin q is perpendicular to the moment arm and thus causes a torque. The horizontal component F cos q is parallel to the moment arm and does not cause a torque. When a torque is applied, rotation occurs around a pivot point, or fulcrum. When more than one torque acts on a body, the acceleration produced is proportional to the net torque.

Center of gravity. See-saw Torque. Motion of a rigid body about its center of mass. Rotational equilibrium. A torque can cause a counterclockwise cc or a clockwise rotation cw. Center of Mass CM The point where all the mass of an object seems to act. For example, if you look at the motion of a high jumper, there is one special spot that moves in a parabolic path. It would be the same point where you could balance that person. An object is in equilibrium as long as its CM is over its base level.

An object is considered uniform when the CM is its geometric center. The CM position is given by:. An analysis of static equilibrium is very important in engineering. The design engineer must identify and isolate all external forces and torques acting on the structure.

With a good design and a correct choice of materials, structures can support loads. Landing gear of aircraft survive the shock of rough landings and bridges don't collapse under traffic loads and the wind. Translational Equilibrium An object is in translational equilibrium its momentum is constant if the sum of the forces acting on it is zero.

Rotational Equilibrium An object is in rotational equilibirum its angular momentum is constant if the sum of the torques acting on it is zero. An object will be in equilibrium if it is suspended from its center of gravity or its center of gravity is below the suspension point. Elasticity The branch of physics which deals with how objects deform when forces are applied to them. Elastic Limit The point where the material being deformed suffers permanent deformation and will not return to its original shape.

There are three ways an object can change its dimensions when forces act on it:. An object can be deformed by shearing forces.

It will behave like the pages of a book when under shear. An example: the movement of layers of rock in an earthquake. An object can be deformed by stretching or compressing forces. An example: tensile forces that stretch the length of a string until it breaks.

An example: Piling weights on a cylinder until it breaks. An fluid can be deformed by bulk forces. An example: A fluid under high pressure can be compressed on all sides resuliting in a volume change.

A stress due to forces produces a strain or a deformation. Stress is proportional to strain and that proportionality cosntant is called its modulus.

Stress is the product of modulus and strain. Stress is the ratio of the force exerted on the object to the cross-sectional area over which the force is exerted. Strain is the resulting deformation, whether it is the ratio of change in length to original length, change in height to original height, or change in volume to original volume. Remember, the ratio of F to A is the pressure P of the fluid. Rotational motion is the motion of an object around an axis.

Up to this point, we have only studied motion in a straight line translational motion. Now we will study motion about an axis, or rotational motion.

Objects can move translationally or rotationally or both. They can be in translational equilibrium the sum of all the forces acting on the object is zero , but not in rotational equilibrium the sum of all the torques acting on the object is zero , and vice versa.

Or, they may be in both rotational and translational equilibrium. Rotational Motion The translational motion of a rigid body is analyzed by describing the motion of its center of mass, as well as rotational motion about its center of mass.

Each particle of a rotating rigid body has, at any moment, a linear velocity v and a linear acceleration a. The angular velocity is the same for every point in the rotating body at any instant, but the linear velocity is greater for points further from the axis of rotation.

In the image below, a body is rotating about a fixed axis through its center. An object placed on the rotating object at point A that rotates to point B rotates through the same angle as an object placed at point a that rotates to point b. Both traveled the same angular distance q. They did not travel the same tangential distance. One traveled the arc length AB in time t while the other traveled the arc length ab in time t.

Angular displacement, q. It is measured in degrees, revolutions, or the SI unit of radians. Note: in rotational motion, it is easy to use the radius to convert back and forth between rotational and translational quantities. It is also easy to remember what to do. Think of the units! If you have a distance in meters, what would you do with the radius also in meters to convert it into radians? You would divide distance in meters by the radius in meters. Meters cancel leaving radians. A radian is a unit that serves as a place holder.

Angular Positon The object has rotated through some angle q when it travels the distance l measured along the circumference of its circular path.

Radian One radian rad is defined as the angle subtended by an arc whose length is equal to the radius. Angular speed or velocity , w. In the image above, the object rotates through angle q in time t. Angular speed velocity can be converted to the analogous translational speed velocity using the radius. Angular acceleration, a. Angular acceleration can be converted to the analogous translational acceleration using the radius.

Anglular Acceleration Angular acceleration is the change in angular velocity divided by the time to make this change. Radial Component of the linear acceleration The total linear acceleration a is the vector sum of the radial component of the acceleration and the tangential component of the acceleration.

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Translational equilibrium 2. Rotational equilibrium 3. Equilibrium problems Back to Course Index. Don't just watch, practice makes perfect. Lessons Notes: In this lesson, we will learn: Meaning of translational equilibrium Solving problems involving translational equilibrium Notes: An object can undergo translational motion motion that changes its position and rotational motion motion that changes its angle.