Question

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

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Solution

## Step 1. Given dataInitial angular velocity ${\omega }_{i}=0rad/sec$Final angular velocity ${\omega }_{f}=20rad/sec$Time $t=5sec$Step 2. Formula usedThe 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 $a=\frac{{\omega }_{f}-{\omega }_{i}}{t}\phantom{\rule{0ex}{0ex}}=\frac{20-0}{5}\phantom{\rule{0ex}{0ex}}=4rad/se{c}^{2}$Step 4. Calculate angular displacementThe angular displacement is$\theta ={\omega }_{i}t+\frac{1}{2}a{t}^{2}\phantom{\rule{0ex}{0ex}}=0+\frac{1}{2}×4×{5}^{2}\phantom{\rule{0ex}{0ex}}=50rad$Step 5. Find the number of revolution Number of revolution is$n=\frac{\theta }{2\pi }\phantom{\rule{0ex}{0ex}}=\frac{50}{2\pi }\phantom{\rule{0ex}{0ex}}=\frac{25}{\pi }$Hence the number of revolution is $\frac{25}{\pi }$.

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