Question

A wheel starts from rest and has angular acceleration of 4 rad/s^2 its angular velocity after 10 revolutions is ?

Answer 1

hey mate here is your answer

now

for 4π rad = 1 revolution

so xπ rad = 10 revolution

X=4×10

angular displacement =40π rad

(final angular velocity)²+(initial velocity)²=2(angular acceleration)(angular displacement)

(Angular velocity)²+0=2(4)(40)

angular velocity=√320

=8√5 rad/sec

hope it will help you

mark me brainliest ✌✌✌

Answer 2

Therefore the angular velocity of the wheel after 10 revolutions is  22.45 rad/s.

Given:

The angular acceleration of the wheel = α = 4 rad/s²

The initial angular velocity of the wheel = ω₁ = 0 rad/s

The number of revolutions = n = 10 revolutions

To Find:

The angular velocity of the wheel after 10 revolutions (ω₂).

Solution:

The given question can be solved as shown below.

1 revolution = 2π rad ⇒ then 10 revolutions = 10 × 2π rad = 20π radians

So the angular displacement of the wheel for 10 revolutions = θ = 20π radians.

Then from Newton's law of motion,

⇒ (Final angular velocity)² - (Initial angular velocity)² = 2 × angular acceleration × angular acceleration

⇒ ω₂² - ω₁² = 2 × α × θ

⇒ ω₂² - 0 = 2 × 4 × 20π

⇒ ω₂² = 160π

⇒ ω₂ = √160π = 22.45 rad/s

Therefore the angular velocity of the wheel after 10 revolutions is  22.45 rad/s.

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