1. A wheel 1 meter in radius accelerates uniformly at 2 rad/s2. Diyar bikin lezkirina goşeyî û ji leza goşeyî of the wheel, 2 seconds later.
Tê zanîn:
Radius (r) = 1 meter
Angular acceleration (α) = 2 rad/s2
Dixwazin: angular acceleration and angular speed after 2 seconds.
Areserî:
(yek) Angular acceleration in 2 seconds
Angular acceleration is constant, thus after 2 seconds, angular acceleration of the wheel is 2 rad/s2.
(B) 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!
Tê zanîn:
The initial angular velocity (ωo) = 0
The final angular velocity (ωt) = 60 rpm = 60 revolutions / 60 seconds = 1 revolution / second = 6,28 radians/second
Navbera demê (t) = 10 saniye
Dixwazin: Angular acceleration (α)
Areserî:
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 = 0.628 rad / s2
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!
Tê zanîn:
Navbera demê (t) = 4 saniye
The initial angular velocity (ωo ) = 20 rad/s
The final angular velocity (ωt) = 10 rad/s
xwest : the magnitude of the angular acceleration (α)
Areserî:
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!
Tê zanîn:
the initial angular velocity (ωo ) = 10 rad/s
the angular acceleration (α) = 2 rad / s2
time interval (t) = 2 seconds
Dixwazin: angle (θ)
Areserî:
θ = 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!
Tê zanîn:
the initial angular speed (ωo) = 20 rad/s
the final angular speed (ωt) = 0
Quncik (θ) = 20 radians
Dixwazin: the magnitude of the angular acceleration (α)
Areserî:
ωt2 = ωo2 + 2 α θ
0 = 202 + 2 α (20)
0 = 400 + 40 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.
Tê zanîn:
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
Dixwazin: Linear speed (v) of point P at t = 10 seconds
Areserî:
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.
Tê zanîn:
The initial angular speed (ωo) = 4 rad/s
Angular acceleration (α) = 0.5 rad/s2
Navbera demê (t) = 4 saniye
Dixwazin: Object’s speed after 4 seconds (ωt)
Areserî:
ωt = ωo + α t
ωt = 4 + (0.5)(4)
ωt = 4 + 2
ωt = 6 rad / s
8. YEK 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
Tê zanîn:
1 saet = 60 deqîqe
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
Dixwazin: Comparison of the number of rounds of the hour needle: the minute needle: the second needle
Areserî:
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
Bersiva rast B e.
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. Hevketin ji hewa
B. Pîvan ji topê
C. Tension force
Areserî:
Qanûna tevgera Newton ya duyemîn 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. Lezkirina navend-sentrîpetal ji ber tê hêza navendî. The centripetal force for this case is the tension force.
Bersiva rast C e.
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