Question

The angular velocity of a circular disc rotating with uniform angular acceleration increases from 20 rad s^-1 to 50 rad s^-1 in a time of 10 seconds. The number of rotations made by the circular disc during this period is:

• A. 125
• B. 150
• C. 175
• D. 200

Hint:

For rotational motion problems, use the kinematic equations similar to linear motion, but with angular quantities like $\omega$, $\alpha$, and $\theta$. To find the number of rotations, divide the total angular displacement by $2\pi$.

Answer 1

The Correct Option is C

Given: Initial angular velocity ω₀ = 20 rad s^-1, final angular velocity ω = 50 rad s^-1, time t = 10 s.
First, calculate the angular acceleration α using ω = ω₀ + α t:
50 = 20 + α (10), so α = 3 rad s^-2.
Next, find the angular displacement θ using θ = ω₀ t + ½ α t²:
θ = (20)(10) + ½(3)(10)² = 200 + 150 = 350 radians.
Finally, convert θ to rotations:
Number of rotations = θ / (2π) = 350 / (2×3.14) ≈ 55.73 rotations.