Define the radian in words.
A chain links the bicycle’s rear wheel and pedals, running round two cogs (toothed wheels), as illustrated in Fig. 1.1. The small cog has radius $0.038\ \text{m}$ and is attached to the rear wheel so that they turn together. The large cog has radius $0.15\ \text{m}$ and is attached to the pedals so that they turn together. The rear wheel has radius $0.46\ \text{m}$. The bicycle is pedalled so that it travels in a straight line at a constant speed of $17\ \text{m s}^{-1}$.
Calculate the rear wheel’s angular speed.
Calculate the rotation period of the small cog.
Show that the distance travelled by point X on the chain in one complete rotation of the small cog is $0.24\ \text{m}$.
Use the result from (b)(iii) to find the angle through which the large cog turns during one complete rotation of the small cog.
The bicycle chain in (b) is transferred to a smaller cog attached to the rear wheel. The bicycle’s speed stays the same. Explain, without calculation, what effect this has on the angular speed of the pedals.