Rotation and Torque PDF

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Practice - Rotation and Torque 1.

A particle is located at r = (4i + 8j + 6k) m. A force F = (16i – 4j)N acts on it. What is the torque, calculated about the origin?

2.

A 1.2 kg particle moving in the xy-plane has momentum p = (3i – 4j) kgm/s. It is located relative to the origin by the position vector r = (1.3i + 6j)m . a. Calculate the angular momentum of the particle with respect to the origin . b. What is the linear velocity of the particle? c. What is the angular speed of the particle about the origin? d. A force F = 7i (N) acting on the particle will produce a torque of what magnitude about the origin? e. The force F= 7i will cause the magnitude of the angular momentum to and the angular speed to .

For 3 – 5: A small rock of mass 3 kg is tied to a cord and spun in a horizontal circle of radius 0.8 m. The tension in the cord has a constant value of 38.4 N. 3.

Find the magnitude of the torque about the fixed end of the cord due to the tension acting on the mass.

4.

Calculate the magnitude of the angular momentum.

6.

Crazy Fred is once again at work in his dungeon. He has kidnapped a poor physics student and has strapped him to a conveyor belt. Hanging from the ceiling, 12 m above the student, is a large rotating saw. The saw is rigged to begin a steady decent once it has reached 12000 rpm. If it starts at rest and accelerates at 2 rad/s2, determine (a) the time it takes the saw to reach the maximum speed and (b) the total time our physics student has to escape if the saw descends at 0.25 m/s.

7.

A 0.68m diameter shaft is turning at 65 rad/s. Thereafter, its angular acceleration is given by α = −10

rad s2

− 5t

rad s3

where t is the elapsed time. (a) Find its angular speed at t = 3.0

s. (b) How far does a point on the edge travel in these 3 seconds?

8.

A 0.3 m radius automobile tire rotates from rest at a constant 2 rad/s2 over a 5 second interval. (a) Calculate the angular displacement. (b) Calculate the centripetal acceleration of a point on the outer edge of the tire at the end of the 5 s interval.

Answers: 1. (24i+96j-144k) mN 2. - (23.2kgm2/s)k; (2.5i-3.33j)m/s; 0.68rad/s; - (42mN) k; increase, increase 3. 0N 4. 7.68 kgm2/s 5. 15.36 J 6. 676.32s 7. 12.5 rad/s, 43.35 m 8. 25 rad, 30 rad/s2...