14. Torque & Rotational Dynamics

Intro to Torque

Multiple Choice
Some trainyards have very large horizontal disks that engines can drive onto, which then rotate to turn the engine around to face the opposite direction. Suppose the train engine is 12 m long and centered at the disk's axis. A 500 N force is applied 5.0 m from the center of the engine, with a rope that makes a $35 °$ angle with the side of the engine. What magnitude torque is being applied to the train engine?
Multiple Choice
Model the propeller of an airplane as a single thin rod, 2.2 m long, with a mass of 80 kg. How much torque is required to bring this propeller from rest to 600 rpm in 2.9 s?
Multiple Choice
You pull with a 100 N at the edge of a 25 cm long wrench, to tighten a bolt (gold), as shown. The angle shown is 53° . Calculate the torque your force produces on the wrench, about an axis perpendicular to it and through the bolt.
Open Question
One force acting on a machine part is F = (-5.00 N)i + (4.00 N)j. The vector from the origin to the point where the force is applied is r = (-0.450 m)i +(0.150 m)j. (a) In a sketch, show r, F, and the origin.
Open Question
A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7).
(a) What torque does the machinist exert about the center of the nut?
Open Question
Calculate the torque (magnitude and direction) about point O due to the force F in each of the cases sketched in Fig. E10.1. In each case, both the force F and the rod lie in the plane of the page, the rod has length 4.00 m, and the force has magnitude F = 10.0 N. (a)
Open Question
A metal bar is in the xy-plane with one end of the bar at the origin. A force F = 97.00 N)i + (-3.00 N)j is applied to the bar at the point x = 3.00 m, y = 4.00 m. (b) What are the magnitude and direction of the torque with respect to the origin produced by F?
Open Question
A metal bar is in the xy-plane with one end of the bar at the origin. A force F = 97.00 N)i + (-3.00 N)j is applied to the bar at the point x = 3.00 m, y = 4.00 m. (a) In terms of unit vectors i and j, what is the position vector r for the point where the force is applied?
Open Question
A machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and he exerts a 17.0-N force at the end of the handle at 37° with the handle (Fig. E10.7). (b) What is the maximum torque he could exert with this force, and how should the force be oriented?
Open Question
(I) A 58-kg person riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?
Open Question
(I) A 58-kg person riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cm.

(b) How could she exert more torque?
Open Question
(II) A potter is shaping a bowl on a potter’s wheel rotating at constant angular velocity of 1.6 rev/s (Fig. 10–59). The friction force between her hands and the clay is 1.8 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 9.0 cm? The moment of inertia of the wheel and the bowl is 0.11 kg • m².
<IMAGE>
Open Question
(II) A particle is located at r → ( 5.0î + 3.5ĵ + 6.0k̂)m. A force F→ = (8.0ĵ - 4.0k̂) N acts on it. What is the torque, calculated about the origin?
Open Question
Force F = ─10ĵ N is exerted on a particle at 𝓇 = (5î＋5ĵ) m. What is the torque on the particle about the origin?
Open Question
In FIGURE EX12.19, for what value of Xaxle will the two forces provide 1.8 Nm of torque about the axle?