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1. The diameter of the dwarf planet, Pluto, is just 2.3 x 106 m. If a space probe were to orbit Pluto near the planet’s surface, what would the arc length of the probe’s displacement be after it had completed eight orbits?

2. Of the solar system’s planets, the one whose orbit around the sun is most circular is Venus. The mean radius of Venus’s orbit is 1.08 x 1011 m. What arc length does Venus travel through when its angular displacement is π/3 rad?

3. The world’s fastest centrifuge attains an average angular speed of 2.65 x 104 rad/s. What was the centrifuge’s angular displacement after 1.5 s?

4. The world’s largest planetarium dome is 30 m in diameter. What would your angular displacement be if you ran around the perimeter of this dome for 120 s with an angular speed of 0.40 rad/s?

5. A grindstone for sharpening knives and axes turns with an angular speed of 10.0 rad/s. If the tangential speed of the grindstone’s rim is 4.60 m/s,what is the radius of a grindstone?

6. A unicycle has a wheel diameter of 40 cm. If the wheel’s average angular acceleration was 2.0 rad/s2, how long would it take for the wheel’s angular speed to increase from 0 rad/s to 9.4 rad/s?

7. A whip 0.56 m long moves in a circle and its angular speed increased from 6.00 rad/s to 6.30 rad/s in 0.60 s, what would the magnitude of the tip’s angular acceleration be? It’s tangential Acceleration?

8. A turntable with an acceleration of 1.5 rad/s2 causes a record to increase its speed to 8 rad/s over a period of 2.5 seconds. What was the initial speed of the record?

9. A lever is used to lift a boulder. The fulcrum is placed 1.60 m away from the end at which you exert a downward force, producing a torque with a magnitude of 400 N·m. If the angle between the force and the lever is 80.0°, what is the applied force?

10. A force is applied to a door at an angle of 45.0° and 1.5 m from the hinge. What force produces a torque with a magnitude of 2 N•m? How large is the maximum torque this force can exert?

11. The object is pivoted at A and two forces act on it as shown. If r1= 1.3 m and r2 = 2.15 m, F1= 4.2 N and F2 = 4.9 N, θ1= 75° and θ2 = 60°, what is the net torque? F1 F2 θ2 θ1 A r1 r2

12. A uniform 40 N board supports two children, one weighing 510 N and the other weighing 350 N. The support is under the center of mass of the board and the 510 N child is 1.5 m from the center. Where should the 350 N child sit to balance the system? What is the normal force acting on the board?

13. A beam of length 10 m, whose mass is 1.8 kg rests w/ its ends on 2 digital scales. A mass (2.7 kg) rests on the beam a distance 2.5 m from the beam’s left end. What is the normal force from each scale? scale scale 10 m

14. A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 205 N and is 3 m long. What is the force each rope exerts on the scaffold when a 675 N worker stands 1 m from the left end?

15. A solid disk with mass of 0.165 kg and radius 0.135 m is spinning at a rate of 30 rad/s and can be stopped in 0.1 s. What is the torque needed to cause the disk to stop in this amount of time?

16. A 30 kg uniform solid cylinder has a radius of 0.18 m. If the cylinder accelerates at a rate of 2.3 x 10-2 rad/s2 as it rotates about its center, how large is the torque acting on it?

17. A 55 kg person stands at the edge of a 6.5 m diameter turntable that has a moment of inertia of 1700 kgm2. The turntable is stationary until the person begins running on the turntable w/ a v = 3.8 m/s. What is the angular velocity of the turntable?

19. A student sits on a rotating stool holding two 3 kg masses. When his arms are extended horizontally the masses are 1 m from the axis of rotation. He rotates with angular speed of 0.75 rad/s, and the moment of inertia of the student-stool is 3 kgm2. The student then pulls the masses to 0.3 m, what is the new angular speed?