A disc starts rotating from rest with constant acceleration and attains an angular velocity of 20 rad s^-1 in 5 seconds. The total angular displacement during this interval is

To calculate the total angular displacement during this interval, we can use the kinematic equation for rotational motion:

Formula:

θ = ω₀t + (1/2)αt²

Where:

• θ is the angular displacement
• ω₀ is the initial angular velocity (0 rad/s since the disc starts from rest)
• t is the time (5 seconds)
• α is the angular acceleration

The angular acceleration can be calculated using the formula:

α = (ω - ω₀) / t

Here:

• ω = 20 rad/s (final angular velocity)
• ω₀ = 0 rad/s (initial angular velocity)
• t = 5 seconds

Substituting the values:

α = (20 - 0) / 5 = 4 rad/s²

Substituting the values into the kinematic equation:

θ = 0 * 5 + (1/2) * 4 * (5)²

θ = (1/2) * 4 * 25 = 2 * 25 = 50 rad

Final Answer:

The total angular displacement during this interval is 50 rad.