Question

A grinding wheel attain a velocity of $20rad/sec$ in $5sec$ starting from rest. Find the number of revolution made by the wheel

Answer 1

Step 1. Given data

Initial angular velocity ${\omega }_i=0rad/sec$

Final angular velocity ${\omega }_f=20rad/sec$

Time $t=5sec$

Step 2. Formula used

The angular acceleration $a=\frac{{\omega }_f-{\omega }_i}{t}$

where ${\omega }_i$ is the initial angular velocity, ${\omega }_f$ is the final angular velocity, $t$ is the time.

Angular displacement $\theta ={\omega }_{i}t+\frac{1}{2}a{t}^2$

Number of revolution $n=\frac{\theta }{2\pi }$

Step 3. Calculate the angular acceleration

The angular acceleration is

$$\begin{gathered} a=\frac{{\omega }_f-{\omega }_i}{t} \\ =\frac{20-0}{5} \\ =4rad/se{c}^2 \end{gathered}$$

Step 4. Calculate angular displacement

The angular displacement is

$$\begin{gathered} \theta ={\omega }_{i}t+\frac{1}{2}a{t}^2 \\ =0+\frac{1}{2}\times 4\times 5^2 \\ =50rad \end{gathered}$$

Step 5. Find the number of revolution

Number of revolution is

$$\begin{gathered} n=\frac{\theta }{2\pi } \\ =\frac{50}{2\pi } \\ =\frac{25}{\pi } \end{gathered}$$

Hence the number of revolution is $\frac{25}{\pi }$.