Question

A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of 5 rad / sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm for 10 seconds. Calculate the change in its angular momentum and change in its kinetic energy​

Answer 1

Answer:0.1 kg/m and 0.625 j

Explanation:

Answer 2

Given info : A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of 5 rad/sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm for 10 sec.

To find : The change in its angular momentum and change in its kinetic energy are ...

solution : m = 8 kg , r = 10cm = 0.1 m , ω₀ = 5 rad/s

torque, τ = 0.01 Nm

we know, Torque , τ = I α

where I is moment of inertia

for flywheel I = 1/2 mr² = 1/2 × 8 × (0.1)² = 4 × 0.01 = 0.04 kgm²

so angular acceleration, α = τ/I

= 0.01/0.04 = 0.25 rad/s²

now final angular velocity, ω = ω₀ + αt

= 5 + 0.25 × 10 = 7.5 rad/s

so change in angular momentum, ∆L = I(ω - ω₀)

= 0.04 × (7.5 - 5)

= 0.04 × 2.5 = 0.1 kgm²/s

change in kinetic energy, ∆K = 1/2 I(ω² - ω₀²)

= 1/2 × 0.04 (7.5² - 5²)

= 0.02 × 12.5 × 2.5

= 0.625 J