Question

QUESTION 3. (3a) Show that - 2mü xi – mū x (W x ) where F is the total force acting on an object of mass m measured by an inertial observer and is the acceleration of the object measured in a frame rotating with angular velocity الها (3b) A bug crawls radially outward with constant speed v from the center of a turntable rotating with constant angular velocity w. Consider a coordinate system fixed to the turntable, in which i points radially outward from the center of the turntable, Â points vertically in the direction of w, and is oriented such that î x j = Ã. Write expressions for the bug's position rand velocity r’in the rotating frame, and use these to write expressions for the coriolis force and the centrifugal force acting on the bug, including their directions (30) The bug's acceleration in the rotating frame is zero; explain briefly why this is true. Use this fact to write an expression for the force exerted on the bug by the turntable, using the equation in part (a) (3d) The force exerted on the bug by the turntable is a force of static friction. Find the distance from the centre of the turntable that the bug can crawl before it begins to slip, if the coefficient of static friction between the turntable and bug is jis

Answer 1

3 (9) In general. idő de 6 + w x хся de fixed at rot 15 - any vector. let G = + w xe ' Elad). ie. To "R d twxr ise I Now let G = 7 Catr + w xp st El pas vy wxh) - dt - R d (VR & WON wx ² ) + dt avi tad (W x H) + w x y te w x W x ² de + w x JR + W X ve twx w x² 2 W X Y w x W x 2) multiply with m F = F - 2mlux ve) - mw x W x 2) Hence Prooved. for RD-

ろしb) 4 = ForG For Fcentrifugal = vi y = rî w=w Feoriolis = -2m (W x ry -am wv (Êxi) am WV (-) (To right of insect) -m w x x (W x 2) = – mw?r (Ex (Exi) ) -mw²r (Exå mw²r (a) (radially outwards) 3169 The Force of Friction acts between bug and surface. E = amukôh + mw'r (-2) borce by Table. so that, Fcor. + ForG + È =0 FExch 3 (0) let distance = r. a Fbriction am wv = F Coso and murr = Esino முஷer FCFG Lecor

F = ung (=ru) W amperew mrow 2 uning coso ung sino tano Divide. mrwa Qmy 2 w w 29 M w 2 tano sq. and add 0 and ② 4 w2 + {²wy = 4 g² 4 Met di² w² uzga 4 let 92 ep ² + r w2 - 1179 2 = 0 M 4 M w²/4 z wty +44 292 2 ½ "/4 +44292 2