Question

For mass 20 kg, torque \( \tau = 5 \, \text{Nm} \), find angular acceleration \( \alpha \).

Hint:

Angular acceleration is found using \( \alpha = \frac{\tau}{I} \), where \( I \) is the moment of inertia. For a point mass, \( I = mr^2 \).

Answer 1

Step 1: Understanding the relationship between torque and angular acceleration.
Torque \( \tau \) is related to angular acceleration \( \alpha \) by the equation: \[ \alpha = \frac{\tau}{I} \] where \( I \) is the moment of inertia. For a point mass, the moment of inertia is given by \( I = mr^2 \), where \( m \) is the mass and \( r \) is the radius or distance from the axis of rotation.
Step 2: Substituting the known values.
Given \( \tau = 5 \, \text{Nm} \) and mass \( m = 20 \, \text{kg} \), we need the radius \( r \) to calculate \( I \). If the radius is provided, we can calculate \( I \) and then use the equation for \( \alpha \).
Step 3: Conclusion.
Thus, the angular acceleration \( \alpha \) can be calculated using \( \alpha = \frac{\tau}{I} \), with \( I = mr^2 \) for a point mass or the appropriate moment of inertia formula for other shapes.