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प्रश्न
A flywheel of a motor has mass 100 kg and radius 1.5 m. The motor develops a constant torque of 2000 Nm. The flywheel starts rotating from rest. Calculate the work done during the first 4 revolutions.
संख्यात्मक
उत्तर
Given:
Mass (m) = 100 kg
Radius (R) = 1.5 m
Torque (τ) = 2000 Nm
Number of revolutions (n) = 4
In linear motion, work done is calculated as:
W = F ⋅ d
W = τ ⋅ θ
Since 1 complete revolution corresponds to 2π radians, for 4 revolutions, the total angular displacement is:
θ = 4 × 2π
θ = 8π radians
π = 3.1416
θ = 8 × 3.1416 = 25.1328 radians
W = τ ⋅ θ
W = 2000 × 25.1328
W = 50265.48 Joules
The work done on the flywheel during the first 4 revolutions is 50,265.48 Joules.
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