A solid wheel starts from rest and undergoes a constant angular acceleration for a…

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

Problem

A solid wheel starts from rest and undergoes a constant angular acceleration

\alpha

for a time interval

t

. Two painted dots, C and D, are located on one spoke of the wheel at radii

r_C

and

r_D

(

r_D > r_C

). Assume

\alpha

t

r_C

, and

r_D

are known. (a) Derive an algebraic expression for the common angular displacement

\theta

of the wheel during the time interval

t

. (b) Using your result from part (a), derive expressions for the linear distances

s_C

and

s_D

traveled by dots C and D during the same interval. (c) Show explicitly that the ratio

\dfrac{s_D}{s_C}

is equal to

\dfrac{r_D}{r_C}

, and explain the physical significance of this result. (d) Suppose

r_D = 0.30\,\text{m}

and

r_C = 0.10\,\text{m}

. If the wheel undergoes an angular acceleration of

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

for

5.0\,\text{s}

, calculate

s_D

and verify that the ratio found in part (c) holds numerically.