A conveyor belt is driven by a cylindrical drum of radius

PHYSICS · Subjective · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

0.50\,\text{m}

. The drum rotates at a uniform rate of

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

. The belt does not slip on the drum. (i) Derive an expression for the linear speed

v

of the belt in terms of the angular speed

\omega

of the drum and its radius

r

. (ii) Using your result from part (i), calculate the linear speed of the belt in

\text{m}\,\text{s}^{-1}

. (iii) How far will a point on the belt move in

15\,\text{s}

at this speed? (iv) If the drum radius is increased by

10\%

while keeping the same angular speed, determine the percentage increase in the linear speed of the belt.