Learning object 1
- 1. JennyGu 11779148 Physics 101 Learning Object Consider a Ferris wheel with a diameter of 20m. Imagine that is plotted on an axis, with the centre of the wheel at the origin (see diagram below). The angular speed of the Ferris wheel is 𝜋 30 sec-1. a. Define angular speed in your own words in relation to a Ferris wheel. b. How long does it take the Ferris wheel to make one full revolution? c. Determine a cosine function of the x-coordinate in terms of time, assuming the starting point is at the lowest point of the Ferris wheel. d. Determine a sine function of the x-coordinate in terms of time, assuming the starting point is at the lowest point of the Ferris wheel. e. Draw the sine/cosine function of the x-coordinate in terms of time. Solution: a. The angular speed (ω) is the rate at which the angle between an initial position and final position is increasing along the path of the Ferris wheel (i.e. the edge of a circle), with the vertex of the angle at the centre of the wheel. In this case, the angle is increasing by a rate of π radians per 30 seconds, or approximately 0.105 radians per second.
- 2. JennyGu 11779148 b. Time for one revolution: T = 2𝜋 𝜔 T = 2𝜋 𝜋 60 = 60 sec. Another way to approach this problem is to think about it logically, if it takes 30 seconds for a compartment on the Ferris wheel to move with a change in angle by π radians, or half a circle, it would take double the time, 60 seconds, to have a change in angle by 2π radians, or a complete circle. c. Radius (R) = 10m Angular speed (ω) = 𝜋 30 sec-1 Starting angle (φ) = 3𝜋 2 x(t) = Rcos(ωt+φ) x(t) = 10cos( 𝜋 30 t + 3𝜋 2 ) d. Because the starting angle is 3𝜋 2 , the cosine graph has been shifted to look like a sine graph with x(0) = 0. Therefore, x(t) can also be written as: x(t) = 10sin( 𝜋 30 t) e. x-axis = time y-axis = x-coordinate Because time cannot be negative (unless it is made relative to a certain initial time), all values of x(t) for t<0 can be disregarded.