The rotation of the 1.2m arm OA about O is defined by the relation ?=0.25t The r

Question

The rotation of the 1.2m arm OA about O is defined by the relation ?=0.25t

The rotation of the 1.2m arm OA about O is defined by the relation ?=0.25t­­­2, where ? is expressed in radians and t in seconds. Collar B slides along the arm in such a way that its distance from O is r=0.8-0.16t2, where r is expressed in meters and t in seconds. After the arm OA has rotated through 30 degree , determine (a) the total velocity of the collar, (b) the total acceleration of the collar, (c) the relative acceleration of the collar with respect to the arm, (d) Coriolis acceleration of the collar B.

Explanation / Answer

theta=0.25t^2

thetadot=0.5t

thata double dot= 0.5

r=0.8-0.16t^2

rdot=0.8t

rdouble dot=0.8

SInce time is not given all velocites and accelaration will be a fuction of time.

a)total velocity of colar= sqrt [(rdot)^2+(r*thetadot)^2]

b) total velocity of accelaration = sqrt { (rdot - r* thetadot^2)^2 + (2 * rdot * thetadot + r *thetadoubledot)^2 }

term in green in radial angular acc.

term in blue is tangentail angular acc.

c)relative velcoty of collar wrt to arm = rdot =0.8t

d)Coriolis acceleration of the collar B = 2 * rdot * thetadot

  

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