Question:

A bicycle wheel starts from rest and undergoes a constant angular acceleration of 2 rad/s^2 for a period of 5 seconds. At the end of this period, the angular velocity of the wheel is measured to be 10 rad/s. Determine the angular displacement of the wheel during this period.

(a) 60 rad

(b) 25 rad

(c) 50 rad

(d) 100 rad

Answer:

Given data: Initial angular velocity, ω_0 = 0 rad/s Angular acceleration, α = 2 rad/s^2 Time, t = 5 s Final angular velocity, ω = 10 rad/s

We can use the formula relating angular velocity, angular displacement, and angular acceleration:

ω = ω_0 + α * t

Simplifying the equation and substituting the given values:

10 rad/s = 0 rad/s + 2 rad/s^2 * 5 s

10 rad/s = 10 rad/s

We see that the final angular velocity matches the given value, indicating that the calculated acceleration is correct.

Next, we can use another formula to find the angular displacement:

θ = ω_0 * t + 1/2 * α * t^2

θ = 0 rad/s * 5 s + 1/2 * 2 rad/s^2 * (5 s)^2

θ = 0 rad + 1/2 * 2 rad/s^2 * 25 s^2

θ = 0 rad + 1 rad * 25 s^2

θ = 25 rad * s^2

Therefore, during this 5-second period, the angular displacement of the bicycle wheel is 25 rad (option (b)).