Question

A wheel has a speed of 1200 revolutions per minute and is made to slow down at a rate of 4 rad/s${}^2$. The number of revolutions it makes before coming to rest is:

• A. 143
• B. 272
• C. 314
• D. 722

Answer 1

Answer: (C)

314

Initial frequency ${\nu }_i=1200$ r.p.m $=\frac{1200}{60}=20$ r.p.s

Initial angular velocity: ${\omega }_i=2\pi {\nu }_i=2\pi \times 20=40\pi$ $rad/s$

Final angular velocity: ${\omega }_f=0$

Using, ${\omega }_f^2-{\omega }_i^2=2\alpha S$

$\therefore$ $0-(40\pi {)}^2=2(-4)S$ $⟹S=200{\pi }^2$ radian

Number of revolutions: $N=\frac{200{\pi }^2}{2\pi }=100\pi \approx 314$