Question

4. (a) Show that mi = F - mw x W x D) - 2mw xi where F is the total force acting on an object of mass m as measured by an inertial observer and ï is the acceleration of the object measured in a frame rotating with constant angular velocity w. Explain briefly the significance of the centrifugal force –mw (w xr) and the Coriolis force -2mw xi. You may use the following relationship: da/dt = a +w xa where da/dt is the rate of change of a vector a as measured by an inertial observer and á is the rate of change of a as measured in a frame rotating at w. (b) Consider a body moving in the northern hemisphere of the earth. The table below gives the direction of the velocity of the body in the left column. Reproduce the table in your answer book and fill the right column with the direction of the Coriolis force in each case. Coriolis Force direction Velocity direction North East South West Up Down (c) A toy aeroplane of mass 5 kg is moving at 20 ms-1 at a latitude of 52° N heading due west. Assume the plane is close to the ground and that the radius of the earth is 6371 km. Find the horizontal and vertical components of the Coriolis force acting on the toy.

Answer 1

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