Question

please can you explain?

17) A bicycle heading west at 2.0 m/s turns 90.0° to the left in 10.0 s. The final velocity of the bicycle after the turn is 4.2 m/s to the south.

Find the direction of the wheel's average angular acceleration. Express your answer as an angle relative to east.

A) 25° south of east

B) 25° north of east

C) 65° north of east

D) 65° south of east

Answer 1

we consider East as +x and North as +y

initial velocity of the bicycle = 2m/s  x - vector form

angular velocity = vR , R is radius of the wheel

angular velocity is perpendicular to the plane of the wheel , points to SOUTH i.e. -y

initial angular velocity _i   = -2R y rads/s

after turning left , linear velocity  v = - 4m/s y  

_f = 4R x rads/s

time interval = 10s

average angular velocity _av = (_f + _i )/2 = 4.2R x - 2R y  

direction of average angular velocity Tan(p) = -2/4.2  

p = -25.46

it is 25^o SOUTH of EAST - (A)