An object's moment of inertia is 2.0 kg m². Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?

Verified step by step guidance

1. Identify the given values: moment of inertia (I) = 2.0 kg m^2, angular acceleration (\(\alpha\)) = 4.0 rad/s^2.
2. Recall the formula for torque (\(\tau\)) related to moment of inertia and angular acceleration: \(\tau = I \cdot \alpha\).
3. Substitute the given values into the formula: \(\tau = 2.0 \, \text{kg m}^2 \cdot 4.0 \, \text{rad/s}^2\).
4. Perform the multiplication to calculate the torque.
5. The result from the calculation gives the net torque in units of Newton meters (Nm).

Key Concepts

Moment of Inertia

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object relative to the axis of rotation. A higher moment of inertia indicates that more torque is required to achieve the same angular acceleration.

Angular Acceleration

Angular acceleration is the rate at which an object's angular velocity changes over time. It is typically measured in radians per second squared (rad/s²). In this question, the angular acceleration is given as 4.0 rad/s², indicating how quickly the object's rotation is speeding up.

Torque

Torque is a measure of the rotational force applied to an object, causing it to rotate about an axis. It is calculated using the formula τ = Iα, where τ is torque, I is the moment of inertia, and α is angular acceleration. Understanding torque is essential for solving problems involving rotational dynamics.