Rotation Practice
1. How many radians of rotation produces a 0.10 m arc of a circle of radius 0.40 m?
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 mouse’s angular acceleration?
a = Dw/Dt
13 rad/s^{2}
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/s^{2}
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 merrygoround 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/s^{2}
b) What is the merrygoround’s tangential acceleration at r = 4.0 m? a = ra
a = 2.1 m/s^{2}
c) What is the merrygoround’s radial (centripetal) acceleration at 1.5 sec?
a = v^{2}/r
v = wr
a = w^{2}r
a = 2.6 m/s^{2}
d) What is the merrygoround’s total linear acceleration at 1.5 sec?
a = 3.3 m/s^{2}
e) What is the frequency of rotation (f) of the merrygoround at t = 1.5 s?
w = 2prad/T .80 rad/s = 2prad/T T =
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