A flywheel rotating at a speed of `600` rpm about its axis is brought to rest by applying a constant torque for `10` seconds. Find the angular deceleration and angular velocity `5` second after the application of the torque.

Explanation

To solve the problem step by step, we will follow these procedures:

### Step 1: Convert the initial angular speed from rpm to revolutions per second.
Given:
- Initial angular speed, \( \omega_0 = 600 \) rpm.

To convert rpm to revolutions per second (rps), we use the conversion factor:
\[ \text{Revolutions per second} = \frac{\text{Revolutions per minute}}{60} \]
Calculating:
\[ \omega_0 = \frac{600 \text{ rpm}}{60} = 10 \text{ rps} \]

### Step 2: Determine the angular deceleration (α).
We know that the flywheel is brought to rest in 10 seconds, which means the final angular speed \( \omega = 0 \) rps after 10 seconds. We can use the equation of motion for angular motion:
\[ \omega = \omega_0 + \alpha t \]
Substituting the known values:
\[ 0 = 10 + \alpha \cdot 10 \]
Rearranging the equation to solve for \( \alpha \):
\[ \alpha \cdot 10 = -10 \implies \alpha = -1 \text{ rps}^2 \]

### Step 3: Find the angular velocity after 5 seconds.
To find the angular velocity at \( t = 5 \) seconds, we again use the angular motion equation:
\[ \omega = \omega_0 + \alpha t \]
Substituting the values:
\[ \omega = 10 + (-1) \cdot 5 \]
Calculating:
\[ \omega = 10 - 5 = 5 \text{ rps} \]

### Summary of Results:
- Angular deceleration \( \alpha = -1 \text{ rps}^2 \)
- Angular velocity after 5 seconds \( \omega = 5 \text{ rps} \)