    Rotation Practice 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

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

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

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

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 mouse’s angular acceleration?

a = Dw/Dt

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

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 = .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

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

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

a = ra

a = 2.1 m/s2

c) What is the merry-go-round’s 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-round’s 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?

T =  Home  