Angular displacement is the angle by which an object rotates in a given time period. It is a vector quantity; hence, it has a magnitude and a direction. The concept of angular displacement in rotational motion tells us how much an object has rotated from its original position. Normally, such angles are given in radians for MDCAT students. It becomes indispensable for solving problems relating to rotational motion—especially those including angular velocity, angular acceleration, and the dynamics of rotating bodies.
Calculating Angular Displacement
The angular displacement
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θ is defined as the change in the angle of rotation from the initial to the final position. It can be calculated as:
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=
????
????
−
∙
????
θ=θ
f
−θ
i
where:
????
????
θ
f
is the final angular position,
????
????
θ
i
is the initial angular position.
For objects in uniform rotational motion, angular displacement is connected with angular velocity and time via the relation:
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=
????
0
????
+
1
2
????
????
2
θ=ω
0
t+
2
1
αt
2
where:
ℬ
0
ω
0
is the initial angular velocity,
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α is the angular acceleration,
????
t is the time.
In the case of uniform angular velocity, that is when acceleration is zero, the equation becomes:
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=
????
????
θ=ωt
where
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ω is the angular velocity, and
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t is the time interval. MDCAT students should be comfortable using these formulas to compute angular displacement in a variety of rotational motion situations.
MDCAT Quiz: Angular Displacement Questions
MDCAT Quiz has often incorporated questions in which students are asked to find angular displacement for the object in rotational motion. Sometimes, students get questions in which they are supposed to find angular displacement using information about the starting and ending angular position of a revolving object. Another approach could be the calculation of an object’s displacement that is undergoing constant angular acceleration or angular velocity. Questions based on the conversion between angular displacement and linear displacement—like the movement of a revolving wheel—have also been repeated over time. Solving the questions needs proper concept understanding of relationships among angular quantities and the appropriateness in the application of relevant formulas.
Free Flashcards for Angular Displacement
Free flashcards are an excellent way for MDCAT students to reinforce their understanding of angular displacement. The flashcards can include the formula for angular displacement, examples of solving problems in angular displacement, and how it relates to other quantities like angular velocity and angular acceleration. If students regularly review these flashcards, then on the MDCAT Quiz, they will be able to quickly recall the necessary equations in order to solve problems relating to angular displacement. Flashcards are useful for consolidating important information and improving one’s skills in problem-solving for rotational motion.
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