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Torque, moment, or moment of force is the tendency of a force to rotate an object about an axis, fulcrum, or pivot.

Moment of inertia is the mass
... more

Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis. The unbalanced torque on a body along axis of rotation ... more

Torque, moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Mathematically, torque is defined as ... more

A knuckle joint is a mechanical joint used to connect two rods which are under a tensile load, when there is a requirement of small amount of flexibility, ... more

Shear stress,is defined as the component of stress coplanar with a material cross section. The average shear stress is force per unit area. Beam shear is ... more

**(a)** The figure shows the forearm of a person holding a book. The biceps exert a force **F _{B}** to support the weight of the forearm and the book. The triceps are assumed to be relaxed.

**(b)**Here, you can view an approximately equivalent mechanical system with the pivot at the elbow joint

Strategy

There are four forces acting on the forearm and its load (the system of interest). The magnitude of the force of the biceps is **F _{B}**, that of the elbow joint is

**F**, that of the weights of the forearm is

_{E}**w**, and its load is

_{a}**w**. Two of these are unknown

_{b}**F**, so that the first condition for equilibrium cannot by itself yield

_{B}**F**. But if we use the second condition and choose the pivot to be at the elbow, then the torque due to

_{B}**F**is zero, and the only unknown becomes

_{E}**F**.

_{B}Solution

The torques created by the weights are clockwise relative to the pivot, while the torque created by the biceps is counterclockwise; thus, the second condition for equilibrium (net **τ = 0**) becomes

Note that **sin θ = 1** for all forces, since **θ = 90º** for all forces. This equation can easily be solved for **F _{B}** in terms of known quantities,yielding. Entering the known values gives

which yields

Now, the combined weight of the arm and its load is known, so that the ratio of the force exerted by the biceps to the total weight is

Discussion

This means that the biceps muscle is exerting a force **7.38** times the weight supported.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the ... more

Stiffness is the rigidity of an object — the extent to which it resists deformation in response to an applied force. In general, stiffness is not the same ... more

A typical small rescue helicopter, like the one in the Figure below, has four blades, each is **4.00 m** long and has a mass of **50.0 kg**. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of **1000 kg**. **(a)** Calculate the rotational kinetic energy in the blades when they rotate at **300 rpm**. **(b)** Calculate the translational kinetic energy of the helicopter when it flies at **20.0 m/s**, and compare it with the rotational energy in the blades. **(c)** To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?

The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.

The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)

Strategy

Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.

Solution for **(a)**

We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find **E _{r}** . The angular velocity

**ω**for

**1 r.p.m**is

and for **300 r.p.m**

The moment of inertia of one blade will be that of a thin rod rotated about its end.

The total I is four times this moment of inertia, because there are four blades. Thus,

and so The rotational kinetic energy is

Solution for **(b)**

Translational kinetic energy is defined as

To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is

Solution for **(c)**

At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:

Discussion

The ratio of translational energy to rotational kinetic energy is only **0.380**. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The **53.7 m** height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.

http://openstaxcollege.org/textbooks/college-physics

Creative Commons License : http://creativecommons.org/licenses/by/3.0/

The Euler’s pump and turbine equations are most fundamental equations in the field of turbo-machinery. These equations govern the power, efficiencies and ... more

Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more

A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend. ... more

The stiffness of a body is a measure of the resistance offered by an elastic body to deformation. A body have a rotational stiffness when it is in a ... more

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more

In engineering, deflection is the degree to which a structural element is displaced under a load. The deflection at any point along the span of an end ... more

Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more

The blade root bending moment due to the wind turbine yaw operation. The yaw rate can be calculated for passive yaw, or is defined by the design for active ... more

Parallel axis theorem ( Huygens –Steiner theorem) , can be used to determine the mass moment of inertia or the second moment of area of a rigid body about ... more

Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass. Moment ... more

Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Elastic deflection is the degree to which a structural element is displaced under a load.

The deflection at any point, along the span of a center
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Moment of inertia is the mass property of a rigid body that defines the torque needed for a desired angular acceleration about an axis of rotation. Moment ... more

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

In physics and applied mathematics, the mass moment of inertia, usually denoted by I, measures the extent to which an object resists rotational ... more

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Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in the figure below, and compare this force with the weight of the forearm plus its load. You may take the data in the figure to be accurate to three significant figures.