A ring of mass 0.8 kg and radius 0.1 m makes (5/π) rotations per second about axis perpendicular to its plane through centre. Calculate angular momentum and kinetic energy of ring.

Question

A ring of mass 0.8 kg and radius 0.1 m makes (5/π) rotations per second about axis perpendicular to its plane through centre. Calculate angular momentum and kinetic energy of ring. (A)  0.08 kg-m2/s,0.2 J  (B)  0.85 kg-m2/s,0.2 J  (C)  0.85 kg-m2/s,0.4 J  (D)  0.08 kg-m2/s,0.4 J

Tardigrade Admin · Accepted Answer

Angular momentum L=I ω=m r2 ω ( text as I=m r2) =0.8 ×(0.1)2 ×(2 π × 5 / π) =0.08 k g-m2 / s Kinetic energy of ring K=(1/2) I ω2 =(1/2) × 0.8 ×(0.1)2 ×(2 π × 5 / π)2 =0.4 J

Q. A ring of mass $0.8 k g$ and radius $0.1 m$ makes $\frac{5}{π}$ rotations per second about axis perpendicular to its plane through centre. Calculate angular momentum and kinetic energy of ring.

$0.08 k g - m^{2} / s, 0.2 J$

$0.85 k g - m^{2} / s, 0.2 J$

$0.85 k g - m^{2} / s, 0.4 J$

$0.08 k g - m^{2} / s, 0.4 J$

Angular momentum
$L = I ω = m r^{2} ω$
$(as I = m r^{2})$
$= 0.8 \times (0.1)^{2} \times (2 π \times 5/ π)$
$= 0.08 k g - m^{2} / s$
Kinetic energy of ring
$K = \frac{1}{2} I ω^{2}$
$= \frac{1}{2} \times 0.8 \times (0.1)^{2} \times (2 π \times 5/ π)^{2}$
$= 0.4 J$

Q. A ring of mass 0.8kg and radius 0.1m makes π5​ rotations per second about axis perpendicular to its plane through centre. Calculate angular momentum and kinetic energy of ring.

0.08kg−m2/s,0.2J

0.85kg−m2/s,0.2J

0.85kg−m2/s,0.4J

0.08kg−m2/s,0.4J