Question

A wheel rotating at $500$ r.p.m. slows down to $400$ r.p.m. at a constant rate of $5rad/s^2$. What is the angular displacement of the wheel? (in rad)

• A. $36.66$
  
• B. $98.5$
  
• C. $97.36$
  
• D. $96.36$
  

Answer 1

Answer: (B)

$98.5$

Initial angular velocity ${\omega }_0=500rpm=500\times \frac{2\pi }{60}rad/s=52.36rad/s$

It reduces its speed by ${\omega }_t=400rpm=41.89rad/s$ and angular retardation $\alpha =5rad/s^2$

Let angular displacement be $\theta$.

${{\Rightarrow \omega }_t}^2={{\omega }_0}^2-2\alpha {\theta }_t{\Rightarrow 41.89}^2={52.36}^2-2\times 5\times \theta \Rightarrow \theta =98.5rad$