torque

Examples of torque in the following topics:

• Torque

  • Torque about a point is a concept that denotes the tendency of force to turn or rotate an object in motion.
  • The torque in angular motion corresponds to force in translation.
  • Clearly, the torque in rotation corresponds to force in translation.
  • Torque can also be expressed in terms of the angular acceleration of the object.
  • Since torque depends on both the force and the distance from the axis of rotation, the SI units of torque are newton-meters.

• Torque on a Current Loop: Rectangular and General

  • Replacing F with IlB in the torque equation gives:
  • Also note that this equation of torque is for a single turn.
  • Maximum torque occurs in (b), when is 90 degrees.
  • Minimum torque is 0, and occurs in (c) when θ is 0 degrees.
  • When loop rotates past =0, the torque reverses (d).

• Relationship Between Torque and Angular Acceleration

  • Torque is equal to the moment of inertia times the angular acceleration.
  • Just like Newton's Second Law, which is force is equal to the mass times the acceleration, torque obeys a similar law.
  • Relationship between force (F), torque (τ), momentum (p), and angular momentum (L) vectors in a rotating system
  • Torque, Angular Acceleration, and the Role of the Church in the French Revolution
  • Express the relationship between the torque and the angular acceleration in a form of equation

• Gyroscopes

  • The forces exerted create a torque that is horizontal toward the person, and this torque creates a change in angular momentum L in the same direction, perpendicular to the original angular momentum L, thus changing the direction of L but not the magnitude of L.
  • The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular to L.
  • This action creates a torque directly toward her.
  • This torque causes a change in angular momentum ΔL in exactly the same direction.
  • Figure (b) shows that the direction of the torque is the same as that of the angular momentum it produces.

• Second Condition

  • The second condition of static equilibrium says that the net torque acting on the object must be zero.
  • If a given object is in static equilibrium, both the net force and the net torque on the object must be zero.
  • To understand what factors affect rotation, let us think about what happens when you open an ordinary door by rotating it on its hinges.The magnitude, direction, and point of application of the force are incorporated into the definition of the physical quantity called torque—the rotational equivalent of a force.
  • In equation form, the magnitude of torque is defined to be τ=rFsinθ where τ (the Greek letter tau) is the symbol for torque, r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force and the vector directed from the point of application to the pivot point.

• Problem-Solving Techniques

  • When solving static problems, you need to identify all forces and torques, confirm directions, solve equations, and check the results.
  • We choose to locate the pivot at the left hand in this part of the problem to eliminate the torque from the left hand.Solution for (a)There are now only two nonzero torques: that from the gravitational force (τw) and that from the push or pull of the right hand (τR).
  • Stating the second condition in terms of clockwise and counterclockwise torques,τcwnet = –τccwnetThat is to say, the algebraic sum of the torques is zero.
  • Here this means:τR = –τwsince the weight of the pole creates a counterclockwise torque and the right hand counters with a clockwise torque.
  • This simplifies things because forces at the pivot point create no torque because of the cross product: $\tau = rF$

• Conservation of Angular Momentum

  • The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
  • Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero.
  • $\vec \tau = \frac{d \vec L}{d t}$, where $\tau$ is the torque.
  • For the situation in which the net torque is zero, $\frac{d \vec L}{d t} = 0$.
  • Her angular momentum is conserved because the net torque on her is negligibly small.

• Rotational Inertia

  • Rotational inertia is the tendency of a rotating object to remain rotating unless a torque is applied to it.
  • In other words, a rotating object will stay rotating and a non-rotating object will stay non-rotating unless acted on by a torque.
  • Recall that torque is the turning effectiveness of a force.
  • In this case, because F is perpendicular to r, torque is simply τ=Fr.
  • So, if we multiply both sides of the equation above by r, we get torque on the left-hand side.

• Static Equilibrium

  • Any region or point, or any static object within a static fluid is in static equilibrium where all forces and torques are equal to zero.
  • The analysis and study of objects in static equilibrium and the forces and torques acting on them is called statics—a subtopic of mechanics.
  • Therefore, the sum of the forces and torques at any point within the static liquid or gas must be zero.
  • Similarly, the sum of the forces and torques of an object at rest within a static fluid medium must also be zero.
  • For a stationary object within a static liquid, there are no torques acting on the object so the sum of the torques for such a system is immediately zero; it need not concern analysis since the torque condition for equilibrium is fulfilled.

• Moment of Inertia

  • Net τ is the total torque from all forces relative to a chosen axis.
  • Such torques are either positive or negative and add like ordinary numbers.
  • This equation is actually valid for any torque, applied to any object, and relative to any axis.
  • As can be expected, the larger the torque, the larger the angular acceleration.
  • For example, the harder a child pushes on a merry-go-round, the slower it accelerates for the same torque.