Question

e Period ( Radius (m) Velocity (m/s) Acceleration (m/) 12T 96π 144π 729π A. 9 m

Answer 1

Circle A :

Period T = 12 $\pi$

we have equation T = 2$\pi$ / $\omega$

2$\pi$ / $\omega$ = 12 $\pi$

$\omega$ = 0.167 rad/sec

using $\omega$ = 2$\pi$r

r = $\omega$ / 2$\pi$

= 0.167 / 2$\pi$

r = 0.0265 m

using V = r $\omega$

V = 0.0265 x 0.167

V = 0.004425 m/sec

using a = V² / r

= 0.004425² / 0.0265

a = 0.0007388 m/sec²

Circle B :

Period T = 96 $\pi$

we have equation T = 2$\pi$ / $\omega$

2$\pi$ / $\omega$ = 96 $\pi$

$\omega$ = 0.021 rad/sec

using $\omega$ = 2$\pi$r

r = $\omega$ / 2$\pi$

= 0.021 / 2$\pi$

r = 0.0033 m

using V = r $\omega$

V = 0.0033x 0.021

V = 0.000693 m/sec

using a = V² / r

= 0.000693² / 0.0033

a = 0.0001455 m/sec²

Circle C :

Period T = 144 $\pi$

we have equation T = 2$\pi$ / $\omega$

2$\pi$ / $\omega$ = 144 $\pi$

$\omega$ = 0.0139 rad/sec

using $\omega$ = 2$\pi$r

r = $\omega$ / 2$\pi$

= 0.0139 / 2$\pi$

r = 0.0022 m

using V = r $\omega$

V = 0.0022 x 0.0139

V = 0.0000306 m/sec

using a = V² / r

= 0.0000306² / 0.0022

a = 0.000000425 m/sec²

Circle D :

Period T = 729 $\pi$

we have equation T = 2$\pi$ / $\omega$

2$\pi$ / $\omega$ = 729 $\pi$

$\omega$ = 0.0027 rad/sec

using $\omega$ = 2$\pi$r

r = $\omega$ / 2$\pi$

= 0.0027 / 2$\pi$

r = 0.00043 m

using V = r $\omega$

V = 0.00043 x 0.0027

V = 0.00000116 m/sec

using a = V² / r

= 0.00000116² / 0.00043

a = 0.00000000313 m/sec²