# Video: Calculating the Magnitude of the Torque on a Wheel of a Train Carriage

The wheel of a train carriage has a moment of inertia of 28 kg.m². As the train is increasing in speed as it leaves the station, the angular acceleration of the wheel is 1.5 rad/s². What is the magnitude of the torque being applied to the wheel?

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### Video Transcript

The wheel of a train carriage has a moment of inertia of 28 kilogram meters squared. As the train is increasing in speed as it leaves the station, the angular acceleration of the wheel is 1.5 radians per second squared. What is the magnitude of the torque being applied to the wheel?

Drawing a diagram can help us visualize the situation. In our diagram, we chose one of the wheels of our train carriage and labeled it with the information from the problem. The moment of inertia, 𝐼, is given as 28 kilogram meters squared. The angular acceleration of the wheel is given as 1.5 radians per second squared. And we are trying to solve for the torque applied to the wheel.

We need an equation that relates these three variables together. We need to remember that Newton’s second law of motion applied to rotational motion is the net torque, 𝜏 net, is equal to the moment of inertia of the object, 𝐼, times the angular acceleration of the object, 𝛼. Looking at our problem, we are given 𝐼, 𝛼, and solving for 𝜏. Therefore, we do not need to rearrange our formula to solve for our unknown variable.

Substituting in our values, we have 28 kilogram meters squared for 𝐼 and 1.5 radians per second squared for 𝛼. When we multiply these two numbers together, we get a 𝜏 of 42 newton meters. The magnitude of the torque being applied to the wheel of the train carriage is 42 newton meters.