Question #123778

A torque of 4Nm is applied to accelerate a wheel from rest to 6rev/sec in a time of 10sec. Determine

(i) angular acceleration

(ii) angular velocity

(iii) angular momentum

(iv) angular impulse

(v) power applied

(i) angular acceleration

(ii) angular velocity

(iii) angular momentum

(iv) angular impulse

(v) power applied

Expert's answer

**Solution.**

"M=4Nm;"

"\\omega_0=0rev\/s;"

"\\omega=6rev\/s;"

"t=10s;"

"\\epsilon=\\dfrac{\\omega-\\omega_0}{t};"

"\\epsilon=\\dfrac{6rev\/s}{10}=0.6rew\/s^2=3.768rad\/s^2;"

"\\omega=6rev\/s=37.68rad\/s;"

"M=I\\epsilon\\implies I=\\dfrac{M}{\\epsilon};"

"I=\\dfrac{4Nm}{3.768rad\/s^2}=1.06kgm^2;"

"L=I\\omega;"

"L=1.06kgm^2\\sdot37.68rad\/s=40kgm^2\/s;"

"P=M\\omega;"

"P=4Nm\\sdot37.68rad\/s=150.72W" ;

**Answer: **"i)\\epsilon=3.768rad\/s;"

"ii)\\omega=37.68rad\/s;"

"iii)I=1.06kgm^2;"

"iv)L=40kgm^2\/s;"

"v)P=150.72W;"

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