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.