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The Rossby number (Ro) named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow. The Rossby number is commonly used in ... more
Is equal to twice the rotation rate of the Earth multiplied by the sine of the latitude
... more
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with ... more
A cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type ... more
A cardioid is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type ... more
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more
A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more
In astrophysics, the Darwin / Radau equation gives an approximate relation between the moment of inertia factor of a planetary body and its rotational ... more
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
Spirograph is a geometric drawing toy that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.
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The Archimedean spiral is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed ... 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.
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Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass.
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The Cissoid of Diocles is a cubic plane curve member of the conchoid of de Sluze family of curves and in form it resembles a tractrix.( Tractix is 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
A banked turn (aka. banking turn) is a turn or change of direction in which the vehicle banks or inclines, usually towards the inside of the turn. For a ... more
Acceleration, in physics, is the rate of change of velocity of an object. An object’s acceleration is the net result of any and all forces acting on ... more
Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more
Spirograph is a geometric drawing toy that produces mathematical roulette curves as hypotrochoids and epitrochoids. A fixed outer circle of radius R is ... more
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 Er . 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/
An epitrochoid is a roulette traced by a point attached to an external circle rolling around the outside of a fixed l circle , where the point is at a ... more
A conical pendulum is a weight (or bob) fixed on the end of a string (or rod) suspended from a pivot. Its construction is similar to an ordinary pendulum; ... more
Uniform circular motion, that is constant speed along a circular path, is an example of a body experiencing acceleration resulting in velocity of a ... more
An epitrochoid is a roulette traced by a point attached to an external circle rolling around the outside of a fixed l circle , where the point is at a ... 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
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
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
The Sagnac effect (also called Sagnac interference), named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is ... more
A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the ... more
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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?