Question

A wheel starts from rest with constant angular acceleration of 2.6 rad/s². During what time will the wheel make one full revolution?

A) 2.6 s
B) 3.14 s
C) 6.28 s
D) 12.57 s

Answer 1

The wheel will make one full revolution in approximately 0.51 seconds.

Step-by-step explanation:

To find the time it takes for a wheel to make one full revolution, we can use the equation:

θ = ω2 / 2α

Where θ is the angle covered, ω is the final angular velocity, and α is the angular acceleration.

Since the wheel starts from rest, the initial angular velocity is 0, and the equation simplifies to:

θ = ω2 / 2α

Since we want to find the time, we can use the equation:

θ = ω2 t / 2α

Where t is the time taken.

For one full revolution, θ is 2π radians. Plugging in the given values:

2π = ω2 t / 2α

α = 2.6 rad/s²

ω = 2π rad/s (since one full revolution is equivalent to 2π radians)

Solving for t:

2π = (2π)2 t / 2(2.6)

t = 2π / (2π)2 * 2(2.6)

t ≈ 0.51 s

Therefore, the wheel will make one full revolution in approximately 0.51 seconds.