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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 data

Initial angular velocity ωi=0rad/sec

Final angular velocity ωf=20rad/sec

Time t=5sec

Step 2. Formula used

The angular acceleration a=ωf-ωit

where ωi is the initial angular velocity, ωf is the final angular velocity, t is the time.

Angular displacement θ=ωit+12at2

Number of revolution n=θ2π

Step 3. Calculate the angular acceleration

The angular acceleration is

a=ωf-ωit=20-05=4rad/sec2

Step 4. Calculate angular displacement

The angular displacement is

θ=ωit+12at2=0+12×4×52=50rad

Step 5. Find the number of revolution

Number of revolution is

n=θ2π=502π=25π

Hence the number of revolution is 25π.


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