A rigid disc rotates about its central axis with an angular velocity

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

\omega

. (i) Starting from the relation between arc length and angular displacement, derive an expression for the linear speed

v

of a point on the rim of radius

r

in terms of

\omega

. (ii) A fan has blades of length

0.30\,\text{m}

and rotates at

1200\,\text{rev\,min}^{-1}

. Calculate the linear speed of the tip of a blade in m s

^{-1}

, taking

\pi = 3.14

. (iii) Another fan of the same angular speed has blades of length

0.45\,\text{m}

. Compare the linear speeds of the tips of the two fans and state the factor by which one exceeds the other.