Video: Calculating the Magnitude of the Torque on a Metal Sphere

A spinning metal sphere has a moment of inertia of 1.7 kg.m². It has a constant angular acceleration of 2.0 rad/s². What is the magnitude of the torque on the object?

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Video Transcript

A spinning metal sphere has a moment of inertia of 1.7 kilograms meters squared. It has a constant angular acceleration of 2.0 radians per second squared. What is the magnitude of the torque on the object?

We have drawn a diagram of our spinning metal sphere with the information given from our problem, including angular acceleration and moment of inertia. To solve for the torque, we need to find a relationship between these three variables. We should recall Newton’s second law of motion for rotational motion, which is the net torque acting on an object, 𝜏 net, is equal to the moment of inertia of the object, 𝐼, times the angular acceleration of the object, 𝛼.

In our problem, we’re given the moment of inertia and we’re given the angular acceleration and asked to find the torque. Therefore, we do not need to rearrange our formula to solve for our unknown variable. Substituting in our values, we see that we are given 1.7 kilograms meter squared for our 𝐼 and we are given 2.0 radians per second squared for our 𝛼. Multiplying these two values together, we get a torque of 3.4 newtons times meters. The magnitude of the torque on the object is 3.4 newton meters.

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