1. What is the angular frequency of a periodic motion with time period T?
A.
T
B.
2πT
C.
2π/T
D.
1/(2πT)
Correct Answer:
2π/T
Explanation:
Angular frequency is related to the time period by ω = 2π/T, where ω is measured in radians per second.
2. What is the SI unit of angular frequency?
A.
hertz
B.
radian per second
C.
second
D.
meter per second
Correct Answer:
radian per second
Explanation:
Angular frequency measures angular change per unit time, so its SI unit is radian per second, written as rad/s.
3. A periodic motion has a frequency of 1 Hz. What is its angular frequency?
A.
1 rad/s
B.
2π rad/s
C.
π rad/s
D.
4π rad/s
Correct Answer:
2π rad/s
Explanation:
Angular frequency is given by ω = 2πf. For f = 1 Hz, ω = 2π rad/s.
4. A particle completes one complete cycle in 2 seconds. What is its angular frequency?
A.
π rad/s
B.
2π rad/s
C.
4π rad/s
D.
1/π rad/s
Correct Answer:
π rad/s
Explanation:
Using ω = 2π/T with T = 2 s, the angular frequency is ω = 2π/2 = π rad/s.
5. Which relation correctly connects angular frequency ω and frequency f?
A.
ω = f/(2π)
B.
ω = 2πf
C.
ω = 2π/f
D.
ω = f + 2π
Correct Answer:
ω = 2πf
Explanation:
One complete cycle corresponds to an angular displacement of 2π radians, so angular frequency is ω = 2πf.
6. If the angular frequency of a periodic motion is 4π rad/s, what is its frequency?
A.
2 Hz
B.
4 Hz
C.
8π Hz
D.
1/(2π) Hz
Correct Answer:
2 Hz
Explanation:
Using f = ω/(2π), f = 4π/(2π) = 2 Hz.
7. If the frequency of an oscillation is doubled, what happens to its angular frequency?
A.
It becomes half
B.
It remains unchanged
C.
It also doubles
D.
It becomes four times
Correct Answer:
It also doubles
Explanation:
Since ω = 2πf, angular frequency is directly proportional to frequency. Therefore, doubling f doubles ω.
8. A periodic function is written as x = A cos(6πt), where t is in seconds. What is its angular frequency?
A.
A rad/s
B.
6π rad/s
C.
3π rad/s
D.
2π rad/s
Correct Answer:
6π rad/s
Explanation:
In the standard form x = A cos(ωt), the coefficient of t is the angular frequency. Therefore, ω = 6π rad/s.
9. What is the angular frequency of a motion having a time period of 1 second?
A.
π rad/s
B.
1 rad/s
C.
2π rad/s
D.
4π rad/s
Correct Answer:
2π rad/s
Explanation:
Using ω = 2π/T and T = 1 s, the angular frequency is 2π rad/s.
10. A periodic motion has an angular frequency of π rad/s. What is its time period?
A.
π s
B.
2π s
C.
1 s
D.
2 s
Correct Answer:
2 s
Explanation:
The time period is T = 2π/ω. For ω = π rad/s, T = 2π/π = 2 s.
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