Question

Dynamic

The 1.0-meter-long horizontal plank shown below rotates with a constant angular velocity of 10 rad/s in the -y direction, while the smaller member (0.5 m long) rotates about the +z axis with a constant angular velocity of 20 rad/s. a. What's the acceleration of the point p at the instant shown? b. If the point p represents an object with a mass of 0.015 kg, what's the net force acting on the object at the instant shown? X p

Answer 1

ny W, =10rced S ye R=1, 51m a = w?r A₂ = W₂²r AR W2=20 rod الي 5 "ai 8=12=0.5 m 1 Z P

both members ( 1 ) a both ازي be ca) Acceleration of point p shorn at this einstant Since rotates with constant ang ular velocity there fore tangential acceleration the members zero. (2) Horizontal planck rotates about point o along ay anuis where an small member rofates about point along positive z-gris. Acceleration of point g with respect to ay = 9, = w2R 102x1 = 100 m to o, aglo S² acceleration of point to with respect to ar = 4₂ = W22r = q, 202x0.5 = 200 aplar 뮤 S?

. By bythagoras theorem, Resultant acceleration of point b ap = 9,²+ a² ap 100? + 2002 alp 223. 607 m s2 ma (6) Net force on object of mass m= 0.015 kg By Newton's and law, Fret = map = 0.015 x 223. 607 Fuer FNet 3-354 N