Online Calculators since 2009
Welcome to our Physics lesson on Power in Rotational Motion, this is the eighth lesson of our suite of physics lessons covering the topic of Dynamics of Rotational Motion, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
The last quantity in which the analogy between translational and rotational quantities is valid, is power. Thus, given that power in translational motion is
we obtain for power in rotational motion
The end of a 60 cm and 300 g rod start rotating from rest rotates in the horizontal plane through a small electric motor around a vertical axis as shown in the figure.
10 s after its start of rotation, the rod gains an angular velocity of 5 rad/s.
a. We must calculate torque and angle of rotation to find rotational work, as he Newton's Second Law of rotational motion is
Moment of inertia I of a bar rotating around its end is
where m = 300 g = 0.3 kg and L = 60 cm = 0.6 m. Thus,
Angular acceleration α is calculated by
where ω = 5 rad/s, ω0 = 0 and t = 10 s. Thus,
(Remember that 1 N = 1 kg × m/s2)
The angle φ wiped by the rod during its rotation is
Hence, the rotational work done by the engine is
b. Angular momentum at the end of 10 s is
Substituting the values we found earlier, we obtain
c. Rotational kinetic energy of the rod at the end of 10 s is
As you see, this value is equal to the work done by the motor to make the rod rotate.
d. Average power delivered by the motor supposing that all energy produced by it, is used to do work, is:
The following table includes everything discussed above regarding the relationship between dynamics translational and rotational quantities and the relevant formulae:
You have reached the end of Physics lesson 7.2.8 Power in Rotational Motion. There are 8 lessons in this physics tutorial covering Dynamics of Rotational Motion, you can access all the lessons from this tutorial below.
|Tutorial ID||Physics Tutorial Title||Tutorial||Video|
|7.2||Dynamics of Rotational Motion|
|Lesson ID||Physics Lesson Title||Lesson||Video|
|7.2.1||Moment of Force as Analogue of Force in Translational World|
|7.2.2||Moment of Inertia|
|7.2.3||Moment of Inertia in Different Systems of Rotational Motion|
|7.2.4||Newton's Second Law for Rotational Motion|
|7.2.6||Work in Rotational Motion|
|7.2.7||Kinetic Energy in Rotational Motion|
|7.2.8||Power in Rotational Motion|
Enjoy the "Power in Rotational Motion" physics lesson? People who liked the "Dynamics of Rotational Motion lesson found the following resources useful:
We hope you found this Physics lesson "Dynamics of Rotational Motion" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.