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Compare positive and negative work done by torque.
Positive work: Energy transferred into the system, speeds it up. Negative work: Energy transferred out of the system, slows it down.
What is the effect of applying a torque in the same direction as the angular displacement?
Energy is transferred into the system, increasing its rotational kinetic energy.
What is the effect of applying a torque in the opposite direction as the angular displacement?
Energy is transferred out of the system, decreasing its rotational kinetic energy.
What happens to the work done if you double the torque?
The work done is doubled.
What happens to the work done if you double the angular displacement?
The work done is doubled.
How do you calculate the work done by a constant torque?
The work done by a constant torque is calculated by multiplying the torque by the angular displacement: $W = \tau \Delta \theta$.
How do you calculate work done by a variable torque?
The work done by a variable torque is calculated by integrating the torque with respect to the angular displacement: $W=\int_{\theta_{1}}^{\theta_{2}} \tau d \theta$.
How do you determine work done from a torque vs. angular position graph?
The work done is equal to the area under the torque vs. angular position curve.
What is the first step to solving a rotational work-energy problem?
Identify all the torques acting on the object and their respective angular displacements.
What is the final step to solving a rotational work-energy problem?
Apply the work-energy theorem or the principle of conservation of energy to relate the work done to the change in rotational kinetic energy.