A construction crew uses a large cylindrical drum to dispense electrical cable
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A construction crew uses a large cylindrical drum to dispense electrical cable. The drum’s radius is not marked. A technician paints a small dot on the outer surface of the drum and observes that, as the cable is pulled off, the dot moves through an arc length of 12.0 m while the drum turns through an angle of 3.00 rad. Assume the cable unwinds without slipping and remains taut.
(a) Determine the radius of the drum.
(b) After additional cable has been removed, the drum is rotating at 2.40 rad s⁻¹. Calculate the speed at which the cable is leaving the drum at this instant.
(c) Suppose the drum decelerates uniformly from 2.40 rad s⁻¹ to rest in 5.0 s. Compute the magnitude of the tangential (linear) acceleration of a point on the rim during this interval.
(d) Discuss whether the linear acceleration found in part (c) would change if the technician’s initial measurement of arc length had been 10 % too large, and justify your reasoning.