Question

Ram goes around a circular track that has a diameter of 8.5 m. If he runs around the track for a distance of 60 m, then determine his angular displacement?
a) 14.12 rad
b) 3.14 rad
c) 12 rad
d) 16 rad​

Answer 1

● Given :-

• Diameter of circular track = 8.5 m.
• Ram’s linear displacement = s = 60 m.

● To determine :-

• His Angular displacement.

● Solution :-

ο First we have to find the radius of circular track that is

${\sf{\implies{Radius = \cfrac{Diameter}{2} }}} \\ \\ {\sf{\implies{Radius = \cfrac{8.5}{2} }}} \\ \\ {\sf{\implies{Radius = 4.25 \: m}}}$

ο Now formula for finding the Angular displacement is and Angluar displacement is .

${\sf{\longmapsto{ \theta = \dfrac{ Distance }{Radius }}}} \\ \\ {\sf{\longmapsto{ \theta = \dfrac{ s }{r }}}} \\ \\ {\sf{\longmapsto{ \theta = \dfrac{ 60}{4.25 }}}} \\ \\ { \underline{ \boxed{ \red{\sf{\longmapsto{ \theta = 14.12 \: radians}}}}}}$

So, option 1 is correct .