1. A wheel 1 meter in radius accelerates uniformly at 2 rad/s2निर्धारित करें कोणीय त्वरण और कोणीय गति of the wheel, 2 seconds later.
ज्ञात :
Radius (r) = 1 meter
Angular acceleration (α) = 2 rad/s2
चाहता था: angular acceleration and angular speed after 2 seconds.
समाधान:
(१) Angular acceleration in 2 seconds
Angular acceleration is constant, thus after 2 seconds, angular acceleration of the wheel is 2 rad/s2.
(ख) Angular speed in 2 seconds
Angular acceleration 2 rad/s2 means the angular speed increases 2 radians/second each 1 second. After 1 second, angular speed = 2 radians/second. After 2 seconds, angular speed = 4 radians/second.
2. A particle accelerates uniformly from rest to 60 rpm in 10 seconds. Determine the magnitude of angular acceleration!
ज्ञात :
The initial angular velocity (ωo) = 0
The final angular velocity (ωt) = 60 rpm = 60 revolutions / 60 seconds = 1 revolution / second = 6,28 radians/second
समय अंतराल (t) = 10 सेकंड
वांछित : Angular acceleration (α)
समाधान:
ωo = the initial angular velocity, ωt = the final angular velocity, α = the angular acceleration, t = time interval, θ = angle.
ωt = ωo + α t
6.28 = 0 + α (10)
6.28 = 10 α
α = 6.28/10
α = एक्सएनयूएमएक्स रेड / एस2
The magnitude of the angular acceleration = 0.628 rad/s2
3. An object slows down from 20 rad/s to 10 rad/s in 4 seconds. Determine the magnitude of angular acceleration!
ज्ञात :
समय अंतराल (t) = 4 सेकंड
The initial angular velocity (ωo ) = 20 rad/s
The final angular velocity (ωt) = 10 rad/s
जरूरत है : the magnitude of the angular acceleration (α)
समाधान:
ωt = ωo + α t
10 = 20 + α (4)
10 - 20 = 4 α
-10=4 α
α = -10 / 4
α = – 2.5 rad/s2
The magnitude of the angular acceleration is -2.5 rad/s2. Negative sign means the object is decelerating. Acceleration = the angular speed increases, deceleration = the angular speed decreases.
4. An object is accelerated for 2 seconds from 10 rad/s to 2 rad/s2. Determine angle rounded by the object!
ज्ञात :
the initial angular velocity (ωo ) = 10 rad/s
the angular acceleration (α) = एक्सएनयूएमएक्स रेड / एस2
time interval (t) = 2 seconds
वांछित : angle (θ)
समाधान:
= ωo + ½ α t2
θ = (10)(2) + ½ (2)(22)
θ = 20 + (1)(4) = 20 + 4
θ = 24 radians
5. A car’s wheel slows down from 20 rad/s to rest after round 20 radians. Determine the magnitude of the angular acceleration of the wheel!
ज्ञात :
the initial angular speed (ωo) = 20 rad/s
the final angular speed (ωt) = 0
कोण (θ) = 20 radians
वांछित : the magnitude of the angular acceleration (α)
समाधान:
ωt2 = ωo2 + 2 α θ
0 = 202 + 2 α (20)
१२ = १० + २ α
400 = – 40 α
α = – 400 / 40
α = – 10 rad/s2
6. A rod PQ with length of 60 cm rotated about point Q as the axis of rotation and PQ as the radius of circle. The rod PQ accelerated from rest to 0.3 rad/s2. What is the linear speed of point P at t = 10 seconds, if the angular initial position is 0.
ज्ञात :
Length of rod PQ = radius of circle (r) = 60 cm = 60/100 m = 0.60 m
The initial angular speed (ωo) = 0 rad/s
Angular acceleration (α) = 0.3 rad s-2
The initial angular position (θo) = 0
वांछित : Linear speed (v) of point P at t = 10 seconds
समाधान:
The final angular speed after 10 seconds :
ωt = ωo + α t = 0 rad/s + (0.3 rad s-2)(10 s) = 3 rad/s
The final linear speed after 10 seconds :
v = r ω = (0.6 m)(3 rad/s) = 1.8 m/s
7. An object rotates with the initial speed of 4 rad/s and the angular acceleration is 0.5 rad/s2. What is the speed of object after 4 seconds.
ज्ञात :
The initial angular speed (ωo) = 4 rad/s
Angular acceleration (α) = 0.5 rad/s2
समय अंतराल (t) = 4 सेकंड
वांछित : Object’s speed after 4 seconds (ωt)
समाधान:
ωt = ωo + α t
ωt = 4 + (0.5)(4)
ωt = 4 + 2
ωt = एक्सएनयूएमएक्स रेड / एस
8. एक wall clock with diameter of 10 cm has three needles, each to show the hours, minutes and seconds. Comparison of the number of rounds of the hour needle: the minute needle: the second needle.
A. 1 : 3 : 180
B. 1 : 12 : 720
C. 4 : 12 : 180
D. 4 : 12 : 720
ज्ञात :
1 घंटा = 60 मिनट
12 hours = (12)(60 minutes) = 720 minutes
Angular speed of the hour needle = 1 revolution / 12 hours = 1 revolution / 720 minutes
Angular speed of the minutes needle = 1 revolution / 1 hour = 1 revolution / 60 minutes
Angular speed of second needle = 1 revolution / 1 minute
चाहता था: Comparison of the number of rounds of the hour needle: the minute needle: the second needle
समाधान:
The equation of circular motion :
Angular speed = number of revolution / time interval
Number of revolution = angular speed x time interval
In the same time interval, for example, 1 minute, how many revolution of hour needle, minute needle, and the second needle.
Number of revolution of the hour needle = angular speed x time interval = (1 revolution / 720 minutes)(1 minute) = 1/720 revolutions
Number of revolution of the minute needle = angular speed x time interval = (1 revolution / 60 minutes)(1 minute) = 1/60 revolutions
Number of revolution of the second needle = angular speed x time interval = (1 revolution / 1 minute)(1 minute) = 1/1 revolution
Comparison of a number of revolutions :
Number of revolution of the hour needle: number of revolution of minute needle : number of revolution of the second needle.
1/720 : 1/60 : 1/1
1/720 : 12/720 : 720/720
1: 12: 720
सही जवाब बी है।
9. A ball tied with a rope. The ball is rotated so that it moves in a circular plane parallel to the surface of the earth. In this motion, the ball accelerates because…..
A. घर्षण हवा का
B. वजन of ball
C. Tension force
समाधान:
न्यूटन की गति का दूसरा नियम states that an object is accelerated if there is a resultant force. The ball is connected to the rope and when the rope rotated, the ball also rotates. When the ball rotates (the ball moves in a circle), the ball undergoes centripetal acceleration. All the moving objects are circular centripetal acceleration. अभिकेन्द्रीय त्वरण के कारण है सेंट्ररपेटल फ़ोर्स. The centripetal force for this case is the tension force.
सही जवाब सी है।
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[wpdm_package id = '439 pack]
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