Mathematics Magazine for Grades 112 



10/2004 



Grade 12Theory:
Chain Rule = f(g) g(x) Proof of f(g(x)) = f(g) g(x) from the definition We can use the definition of the derivative:
Therefore, f(g(x)) can be written as such: f(g(x)) = =
=
=
Solutions from the Previous Issue:1. A bicycle wheel of radius r = 1.5 m starts from rest and rolls 100 m without slipping in 30 s. Calculate a) the number of revolutions the wheel makes, b) the number of radians through which it turns, c)The average angular velocity. Solution: a) If there is no slipping, the arc length through which a point of the rim moves is equal to the distance traveled, so that the number of revolutions is: n = = 10.6. b) c) Average angular velocity: 2. Assuming that the angular acceleration of the wheel given above was constant, calculate: a) The angular acceleration, b) the final angular velocity c) the tangential velocity and tangential acceleration of a point on the rim after one revolution. Solution: a) For constant angular acceleration: Using and solving for α gives: b) c) After one revolution, Δθ = 2π. Using we get . The tangential velocity and acceleration are: and
Proposed Exercises: 
