Part A What angle in radians is subtended by an arc of 1.60 m in length on the c

Question

Part A
What angle in radians is subtended by an arc of 1.60 m in length on the circumference of a circle of radius 2.54 m ?

=
  rad  

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Part B
What is this angle in degrees?

=
    

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Part C
An arc of length 13.8 cm on the circumference of a circle subtends an angle of 122 . What is the radius of the circle?

r =
  cm  

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Part D
The angle between two radii of a circle with radius 1.51 m is 0.710 rad . What length of arc is intercepted on the circumference of the circle by the two radii?

L =
  m  

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Question #2

A bicycle wheel has an initial angular velocity of 2.10 rad/s .Part A

If its angular acceleration is constant and equal to 0.200 rad/s2, what is its angular velocity at t = 2.50 s?

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Part B

Through what angle has the wheel turned between t = 0 and t = 2.50 s?

Express your answer with the appropriate units.

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QUESTION #3

An electric fan is turned off, and its angular velocity decreases uniformly from 470 rev/min to 170 rev/min in a time interval of length 4.40 s .

Part A

Find the angular acceleration in rev/s2.

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Part B

Find the number of revolutions made by the motor in the time interval of length 4.40 s .

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Part C

How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part A?

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Explanation / Answer

1)

A) s = *r
1.60 m = * 2.54m
= 0.629 rads

B)

=0.629rads * 180º/rads =36º

C)

13.8 cm = 122º * rads/180º * r
r =6.48 cm

d)

arc length = r

Think of it this way, if the angle was 2 radians (or 360°, an entire circle), the arc length would be 2r - the circumference of a circle!

arc length = (1.51)(0.71) =1.07m

2)

For this you will need kinematics
i = 2.10 rad/s
= 0.200 rad/s^2
t = 2.50 s
a)

= i + t
= 2.10 + (0.200)(2.50)
= 2.10 + 0.5
= 2.6 rad/s
b)
= i(t) + 2t
= (2.10 * 3) + (2*0.200*2.50)
= 6.3 +1
=7.3 rad

3)

470 rpm = 470/60 rev/s =7.8rev/s
170 rpm =2.8 rev/s
a)
Ang accel = (f - i) / t = (2.8 - 7.8) / 4.40 rev/s^2 = -1.13 rev/s^2

b)

Nr of revs =2.8 rev/s * 4.40s + (0.5 * -1.13 * 4.40^2) = 1.38 revs

c)

Time to stop = ang accel = (0 - i) / a = -2.8 / -1.13 s = 2.47 s

(same time as it took to reduce the speed by half from1.38to 2.8 rev/s)

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