
If is the frequency of rotation of a body, its angular velocity is ____.
A. 2πn
B. 4πn
C. 6πn
D. πn
Answer
442.8k+ views
Hint:To understand the relationship between angular velocity and frequency, we need to dig deeper into the definition of angular velocity. Also establishing a mathematical relation is the main goal.
Complete answer:
At a given time period, the number of rotations made by a rotating object around a centre is the angular velocity of that object. Whereas frequency is the number of revolutions that an object makes per some given unit of time.
Therefore, if an object makes one full revolution, then its frequency will be measured in terms of . And the angular velocity is the number of radians per some given unit of time, that is, .Now, the relation between revolution and radians is that one revolution is radians per second.
Therefore, the relation of frequency in terms of radians becomes per the second square, but angular velocity in terms of radians is radians per second and so the frequency becomes angular velocity by . So, if angular velocity is and frequency is (as per the question), the relation becomes , that is the angular velocity will be .
Hence, the correct answer is option A.
Note:Both angular velocity and frequency can be expressed in terms of time period too. This way we can relate both angular velocity and frequency with their mathematical terms and generate two different equations with the me period of a rotating object.
Complete answer:
At a given time period, the number of rotations made by a rotating object around a centre is the angular velocity of that object. Whereas frequency is the number of revolutions that an object makes per some given unit of time.
Therefore, if an object makes one full revolution, then its frequency will be measured in terms of
Therefore, the relation of frequency in terms of radians becomes
Hence, the correct answer is option A.
Note:Both angular velocity and frequency can be expressed in terms of time period too. This way we can relate both angular velocity and frequency with their mathematical terms and generate two different equations with the me period of a rotating object.
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE

Give two reasons to justify a Water at room temperature class 11 chemistry CBSE
