8/16/2019 Rotation Bridge

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Rotation Bridge The purpose of the sheet to bridge the τ = Iα stuff with the F = ma stuff. The bridge willalways be a = αr. The basic set up for any problem is “two euations! two un"nowns#with the understanding that a = αr $or α = a%r& can be substituted anywhere as needed.

'uation () τnet = Iα $For e*ample! it might be something li"e $rT& = $+,r-&$α&'uation -) Fnet = ma. $For e*ample! it might be T mg = ma&

'/er present bridge) a = αr $or α = a%r&0( 1 bloc" of mass 2"g is hanging on a pulley%wheel that can be assumedto be a cylinder. The radius of the wheel is .3m. The ultimate uestion iswhat is the acceleration of the falling bloc" $and all the "inematics that goeswith it&. I will brea" it down)

(& 4rite a general formula for the torue-& 4rite a general formula for the Force2& 4hat euation bridges the two53& Ta"e your time. 6o “- euations! - un"nowns# and 7nd a

$acceleration&8& If possible! 7nd T. $I split this up because you must 7nd “a# to

proceed. 9ometimes you need T and sometimes you don:t.

;& ow long does it ta"e the bloc" to hit the ground5?& $Ignore the (m for this one& >ow far does the bloc" fall

in the 7rst .; sec5

0- 1 bloc" of mass -"g is hanging on a pulley%wheel that can beassumed to be a 9@>'R'. The radius of the wheel is .2m. There is alsoan applied force on a rope as labeled. The applied force is 3A.

(& 4rite a general formula for the torue

-& 4rite a general formula for the Force2& 4hat euation bridges the two53& Find a.

02 1 pulley%wheel $cylinder& is on a rope as shown. The mass of the wheelis "g and the radius is .; m.

(& If the wheel is held in euilibrium what is the force in eachrope5 4hat is T and Fapp5

For the rest of the problem, assume that there is an applied force pulling upon the right and the wheel is rotating CCWand the center of mass of the

wheel is moving upward.-& 4rite a general formula for the torue2& 4rite a general formula for the Force $?:mon! you can do this.

Cnly loo" at linear forces. There are two up and one down.&3& 4hat euation bridges the two58& The applied force is 88A;& Find a.& For fun! 7nd T! but “a# is much more important because you

need it for the Big 2.D& ,a"e a comment about how the Big 2 can be used to 7nd

things li"e Ef! t! d! etc. if gi/en some info.

8/16/2019 Rotation Bridge

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