Question

A circular drum of radius 20 cm is initially rotating at 800 rev/min. It is then brought to a stop after making 40 revolutions. What is the angular acceleration?

Answer 1

The angular acceleration can be determined using the kinematic equation for rotational motion, considering the initial angular velocity, the final angular velocity (zero), and the angle rotated in radians.

Step-by-step explanation:

To find the angular acceleration of a circular drum that is brought to a stop after making 40 revolutions, we can use kinematic equations for rotational motion. We know:

• Initial angular velocity (ω0) = 800 rev/min = 800 x π/30 rad/s (since 1 rev = 2π rad and 1 min = 60 s)
• Final angular velocity (ω) = 0 rad/s (since the drum is brought to a stop)
• Number of revolutions made = 40 rev = 40 x 2π rad

Using the equation ω2 = ω02 + 2αΘ, where Θ is the total angle in radians and α is the angular acceleration, we can solve for α:

0 = (ω0)2 + 2α(40 x 2π)
α = -(ω0)2/(2 x 40 x 2π)

After plugging in the values and calculating, you can find the magnitude of the angular acceleration.