Question

A popular game in villages is to roll a cycle tyre with astick. Let’s assume that the tyre has a diameter of 40cm and makes 10 revolutions per second, what will beits forward speed?Hint: In one revolution, the tyre will cover the distanceequal to the perimeter of the tyre. The perimeter of a circle is roughly 3.14times its diameter

Answer 1

Given:

The diameter of the tire is 40 cm.

∴ d =cm

The cycle makes 10 revolutions per second.

∴ f =  10 Hz

To find:

Speed of cycle =?

Explanation:

To roll a cycle tire with a stick, a tier travels circularly.

∴ The angular velocity of the tier is ω.

∴  ω = $\displaystyle \frac{\theta}{t}$

But Ф = $\frac{S}{r}$

∴ $\displaystyle \omega = \frac{S}{rt}$

Now S = perimeter of circle = 2$\pi$r

∴ $\displaystyle \omega = \frac{2\pi r}{rt} \\\\\displaystyle \omega = \frac{2\pi }{t}$

∴ ω = 2$\pi$f

∴ ω = 2 × 3.14  ×10

∴ ω = 62.8 rad/s