Calculating torque if the mass given?

To calculate torque, you need to know the force applied and the distance from the point of rotation where the force is applied. The formula for torque is:

Torque = Force x Distance

If the mass is given, you can calculate the force applied by using the formula:

Force = Mass x Acceleration

Once you have the force and the distance, you can calculate the torque by multiplying the force by the distance.

Formula:

```
Torque (τ) = Moment of Inertia (I) - Angular Acceleration (α)
```

Steps:

1. Determine the moment of inertia (I):
- For a rigid body, the moment of inertia depends on the mass distribution and the axis of rotation. Use the appropriate formula for the shape and size of the object.
- For a point mass rotating about an axis at a perpendicular distance "r", the moment of inertia is:
```
I = mr^2
```

2. Determine the angular acceleration (α):
- If the mass is rotating about a fixed axis, the angular acceleration is the second derivative of the angular displacement (θ) with respect to time (t):
```
α = d²θ/dt²
```

3. Calculate the torque (τ):
- Once the moment of inertia and angular acceleration are known, the torque can be calculated using the formula given above:
```
τ = I - α
```

Example:

A point mass of 2 kg is rotating about an axis at a perpendicular distance of 0.5 m. If the angular acceleration is 2 rad/s², calculate the torque acting on the mass.

Solution:

1. Moment of Inertia:
```
I = mr^2 = (2 kg) - (0.5 m)^2 = 0.5 kgm²
```
2. Angular Acceleration:
```
α = 2 rad/s²
```
3. Torque:
```
τ = I - α = 0.5 kgm² - 2 rad/s² = 1 Nm
```

Therefore, the torque acting on the mass is 1 Nm.