Kinesiology 3341A/B Lecture Notes - Lecture 7: Angular Acceleration, International System Of Units, Angular Displacement

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5 Nov 2016

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How mass is distributed to allow rotation rather than the amount of mass. The further from center of rotation, the harder it is to rotate. Angular equivalents hold just like f = ma. The greater the mass, the greater the force must be to cause a given acceleration. The greater the inertia, the greater the moment must be to cause a given angular acceleration. For point masses: (mass concentrated into a point) If you know m and d from point of rotation- can calculate moment of inertia. Com for each slice and r- then add up m(r2) to get i. If you know moment of inertia then add mass with distance, can calculate any moment of inertia. Hydrostatic weighing put limb in water- can figure out density of each segment and use that time of approach. Choking up on bat- bring mass close to hands. Green - i = mr2 all of its mass with big radius.

Related Questions

x.Hm

I just need help in the three questionI figure the last question

1)Consider an oxygen molecule (O2) rotating inthe xy plane about the z axis. The axis

passes through the center of the molecule,perpendicular to its length. The mass of each

oxygen atom is 2.66 x 10

-26 kg, and at room temperature the average separation between

the two atoms is

d=1.21 x 10-10 m (the atoms are treated as point masses).a) Calculate

the moment of inertia of the molecule about the zaxis. b) If the angular speed of the

molecule about the

z axis 4.60 x 1012 rad/s, what is its rotational kineticenergy?

Answer: a) 1.95 x 10

-46 kg.m2 b) 2.06 x 10-21 J

2) A wheel rotates with a constant angularacceleration of 3.50 rad/s2. If the angular speed

of the wheel is 2.00 rad/s at

ti = 0, a) through what angle does the wheel rotate in2.00 s?

Answer a) 6300

3)A uniform rod of length L and mass M is free to rotate on africtionless pin passing

through one end as shown in question 4 below. Therod is released from rest in the

horizontal position. a) What is its angular speedwhen it reaches its lowest position?

b) Determine the linear speed of the center ofmass and the linear speed of the lowest

point on the rod when it is in the verticalposition.

Answer: a)

3g b) Center of mass speed =3gL

1 ;

Linear speed of the lowest point =3gL

(Hint, use mechanical energy conservation)

4 A uniform rod of length L and mass M is attached at one endto a frictionless pivot and is

free to rotate about the pivot in the verticalplane, as shown in Figure below. The rod is

released from rest in the horizontal position. a)What is the initial angular acceleration of

the rod and b) the initial linear acceleration ofits right end? Answer: a)

Answer: a)

g b) Center of mass speed = 3gL

1 ;

Linear speed of the lowest point =3

(Hint, use mechanical energyconservation)

Astrophysicists in the 1960s tried to explain the existence and thestructure of pulsars â extremely regular astronomical sources ofradio pulses whose periods ranged from seconds to milliseconds. Atone point, these radio sources were given the acronym LGM, standingfor âLittle Green Men,â a reference to the idea that they might besignals of extraterrestrial civilizations. The explanation giventoday is no less interesting. Consider the following. Our Sun,which is a fairly typical star, has a mass of 1.99x10^30 kg and aradius of 6.69x10^8 m. Although it does not rotate uniformly,because it isnât a solid body, its average rate of rotation isabout 1 rev / 25 days. Stars larger than the sun can end theirlives in spectacular explosions called supernovae, leaving behindcollapsed remnants of the stars called neutron stars. Neutron starshave masses comparable to the original masses of the stars, butradii of only a few kilometers. These stars emit beams of radiowaves. Because of the rapid angular speed of the stars, the beamssweep past Earth at regular, very short, intervals. To produce theobserved radio-wave pulses, the star has to rotate at rates fromabout 1 rev/s to 1000 rev/s.

a. Estimate the rotation rate of the Sun if it were to collapseinto a neutron star of radius 10 km. The Sun is not a uniformsphere of gas, and its moment of inertia is given by I = 0.059MR2.Assume that the neutron star is spherical and has a uniform massdistribution.
b. Is the rotational kinetic energy of our Sun greater of smallerafter the collapse? By what factor does it change, and where doesthe energy go to or come from?

Docking bay: A space station consists of a large circular ringof mass m_r and radius R, connected by thin spokes (ofnegligible mass) to a tiny (negligible size) but dense (notnegligible mass) central hub of mass m_h. Initially, thestation is at rest, neither translating nor rotating. An unpoweredspace pod of mass m_p (much smaller than m_r )drifts through space with speed v_p, approaching a spacestation on a path exactly tangential to the ring. As the podtouches the ring, the station's docking mechanism suddenly grabs itand holds it in place at that point on the ring.

a.) What is the station's moment of inertia about its hub beforethe pod docks?

b.) As the pod approaches the station, what is its angularmomentum relative to the station's hub?

c.) After the pod docks, at what rate (in radians/sec) does thestation rotate?

For the remainder of this problem, use "Ï" as the station'sangular velocity after docking no matter what answer you found forpart (c).

d.) What apparent weight would a person in the pod feel becauseof this rotation?

e.) The station has rotational thrusters: jets located aroundthe outside of the ring, pointed tangentially to control therotation of the station. How much work must these jets do on thestation in order to stop the rotation?

f.) If the station has four jets, located 90^o apartaround the ring and each capable of exerting a tangential force Fon the station, what total torque can they apply?

g.) How much time will the jets require to stop therotation?

Kinesiology 3341A/B Lecture Notes - Lecture 7: Angular Acceleration, International System Of Units, Angular Displacement

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