Preparation for circular motion tutorial 12 to 14.
12. a) To answer this explanation you have to show free body diagram for 2 locations : top and bottom. Write the equation to proof that the tension is greater at that location.
b) Since angular speed (w )is required , write the equation at the specific location using the tension T = 20N .
c) The speed (v= rw) is tangential , so a horizontal velocity is given to the stone. Using the kinematics , solve the projectile problem.
13. I have discussed this train scene in class and ask you to look at the rings on the ceiling of you bus or train. Draw a pendulum diagram for each of the parts a), b) and c). Indicate the direction of motion of the diagram a) and b) . Indicate the centre of the circle for diag c).
Draw free body diagram for case c) and solve the tan angle formula, to solve for speed of train.
14. Locate the radius of the circle and find its value.
Draw a free body diagram of the passenger (not the seat) . Write the equation in x and y comp. You will end up with a familiar tan angle formula.
Calculate rate of rotation w.
T cos @= mg...(1) Tsin @ = mw2r...(2)
when w is reduced at a particular radius r, by equation (2) T is reduced. By equation (1) if T is reduced cos @ is increased as mg is constant. Hence @ is reduced (cos 0 = a max value). Eventually the angle becomes 0 when it stops.
