To solve this problem, we need to use the principles of rotational motion.

First, we need to calculate the torque (τ) produced by the force. Torque is given by the formula τ = F*r, where F is the force and r is the radius of the disk.

τ = 20 N * 0.2 m = 4 Nm

Next, we need to calculate the moment of inertia (I) of the disk. For a uniform circular disk, the moment of inertia is given by the formula I = 0.5*m*r^2, where m is the mass of the disk and r is its radius.

I = 0.5 * 20 kg * (0.2 m)^2 = 0.4 kg*m^2

Now, we can use the relation between torque, moment of inertia, and angular acceleration (α), which is given by the formula τ = I*α. Solving for α, we get:

α = τ / I = 4 Nm / 0.4 kg*m^2 = 10 rad/s^2

The final angular speed (ω) is given as 50 rad/s. The initial angular speed (ω0) is 0 rad/s (since the disk is initially at rest). We can use the formula ω = ω0 + α*t to find the time (t) it takes for the disk to reach the final angular speed.

50 rad/s = 0 rad/s + 10 rad/s^2 * t

Solving for t, we get t = 5 s.

Finally, we can calculate the number of revolutions (n) the disk makes in this time. The angular displacement (θ) is given by the formula θ = ω0*t + 0.5*α*t^2. Substituting the known values, we get:

θ = 0 rad/s * 5 s + 0.5 * 10 rad/s^2 * (5 s)^2 = 125 rad

Since one complete revolution corresponds to 6.28 rad, the number of revolutions is given by n = θ / 6.28.

n = 125 rad / 6.28 rad/revolution ≈ 20 revolutions

So, to the nearest integer, the disk makes 20 revolutions to attain an angular speed of 50 rad/s.

Question

To solve this problem, we need to use the principles of rotational motion.

First, we need to calculate the torque (τ) produced by the force. Torque is given by the formula τ = F*r, where F is the force and r is the radius of the disk.

τ = 20 N * 0.2 m = 4 Nm

Next, we need to calculate the moment of inertia (I) of the disk. For a uniform circular disk, the moment of inertia is given by the formula I = 0.5*m*r^2, where m is the mass of the disk and r is its radius.

I = 0.5 * 20 kg * (0.2 m)^2 = 0.4 kg*m^2

Now, we can use the relation between torque, moment of inertia, and angular acceleration (α), which is given by the formula τ = I*α. Solving for α, we get:

α = τ / I = 4 Nm / 0.4 kg*m^2 = 10 rad/s^2

The final angular speed (ω) is given as 50 rad/s. The initial angular speed (ω0) is 0 rad/s (since the disk is initially at rest). We can use the formula ω = ω0 + α*t to find the time (t) it takes for the disk to reach the final angular speed.

50 rad/s = 0 rad/s + 10 rad/s^2 * t

Solving for t, we get t = 5 s.

Finally, we can calculate the number of revolutions (n) the disk makes in this time. The angular displacement (θ) is given by the formula θ = ω0*t + 0.5*α*t^2. Substituting the known values, we get:

θ = 0 rad/s * 5 s + 0.5 * 10 rad/s^2 * (5 s)^2 = 125 rad

Since one complete revolution corresponds to 6.28 rad, the number of revolutions is given by n = θ / 6.28.

n = 125 rad / 6.28 rad/revolution ≈ 20 revolutions

So, to the nearest integer, the disk makes 20 revolutions to attain an angular speed of 50 rad/s.

Knowee AI · Accepted Answer