Problem — Wheel at 40 revolutions per minute

Problem

A wheel of radius $8{,}0\;\mathrm{cm}$ makes $40$ revolutions per minute. Calculate its angular velocity and the linear velocity of a point on the rim.

Solution

Each revolution is $2\pi$ radians; $40$ revolutions per minute correspond to $40/60$ revolutions per second. $\omega = \frac{40\cdot 2\pi}{60\;\mathrm{s}} \approx \ev{4{,}19\;\mathrm{rad/s}}$ The linear velocity of a point on the rim (radius $R = 0{,}080\;\mathrm{m}$): $v = \omega R = 4{,}19\cdot 0{,}080 \approx \ev{0{,}33\;\mathrm{m/s}}$

Links

Topics: Rotational dynamics Concepts: Angular velocity Objects: Rotating disc