A tennis-ball machine uses two identical wheels to launch balls

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A tennis-ball machine uses two identical wheels to launch balls. Each wheel of radius

0.10\,\text{m}

spins up uniformly from rest to

3.0\times10^{3}\,\text{rev}\,\text{min}^{-1}

2.0\,\text{s}

. At the same sports facility, a mechanical cart on a straight track accelerates uniformly from rest so that its speed matches the tangential speed of the wheel rims exactly at the

2.0\,\text{s}

mark. Respond to all parts thoroughly, expressing final answers with appropriate significant figures and units. (a) Calculate the wheel’s constant angular acceleration in

\text{rad}\,\text{s}^{-2}

. (b) Determine the linear (tangential) speed of a point on the rim at

t=2.0\,\text{s}

. (c) Find the constant linear acceleration required for the cart to reach the speed found in part (b) in the same time interval. (d) Compute the cart’s linear displacement during the

2.0\,\text{s}

acceleration and compare this value to the total angular displacement (in radians) of a point on the rim during the spin-up. Discuss the similarity or difference in the mathematical structure of the two results.

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