Rotation Practice

radianPic

1. How many radians of rotation produces a 0.10 m arc of a circle of radius 0.40 m?

 

q = d/r

 

 

q = .10m/.40 m

 

 

q = .25 radians

 

 

2. How many degrees of rotation is produces a 0.10 m arc of a circle of radius of 0.40 m?

 

.25 radians[360/2prad]

 

 

 

3. A ball rotates 2P  radians in 4.0 s.  What is its angular velocity?

 

w = 2Pradians/4 sec

 

w = 1.6 radians/sec

 

 

4. A toy car rolls in a circular path of radius 0.25 m and the car wheels rotate an arc length of 0.75 m in 8.0 s. 

What is the angular velocity of the wheels?

 

v = .75 m/8.0 sec

 

v = .094 m/s

 

v = wr

w = v/r

 

w = .38 rad/s

 

5. A mouse is running around in a circle.  It starts from rest and accelerates to ω = 12 rad/s in 0.90 s.  What is the mouseís angular acceleration?

 

a = Dw/Dt

 

 

13 rad/s2

 

 

6. A bicycle tire moving at ω = 3.5 rad/s accelerates at a constant rate to 4.2 rad/s in 3.0 s.  What is its angular acceleration?

 

a = Dw/Dt

 

 

 

a = .23 radians/s2

 

 

 

7. A bicycle with tires of radius equal to 0.30 m is moving at a constant angular velocity of 2.5 rad/s. 

What is the linear velocity of the bicycle?

v = wr

v = 2.5 radians/s[.30m]

 

v = .75 m/s

 

8. A motorbike has tires of radius 0.25 m. If the motorbike is traveling at 4.0 m/s, what is the angular velocity of the tires?

 

v = wr

 

w = v/r

 

w = 16 radian/sec

 

9. An elementary school student pushes, with a constant force, a merry-go-round of radius 4.0 m from rest to an angular velocity of 0.80 rad/s in 1.5 s. 

 

a) What is the angular acceleration, α?

a = Dw/Dt

a = -.80rad/s/1.5 sec

a = .53 rad/s2

 

b) What is the merry-go-roundís tangential acceleration at r = 4.0 m?

a = ra

 

a = 2.1 m/s2

 

 

c) What is the merry-go-roundís radial (centripetal) acceleration at 1.5 sec?

 

a = v2/r

 

v = wr

 

a = w2r

 

a = 2.6 m/s2

 

 

d) What is the merry-go-roundís total linear acceleration at 1.5 sec?

 

 

 

a = 3.3 m/s2

 

e) What is the frequency of rotation (f) of the merry-go-round at t = 1.5 s?

 

w = 2prad/T

 

.80 rad/s = 2prad/T

T =
 

 

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