14. Torque & Rotational Dynamics

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.

(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?

(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?

(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.

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(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?

(II) The bolts on the cylinder head of an engine require tightening to a torque of 95 m • N.

(a) If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?

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(II) The bolts on the cylinder head of an engine require tightening to a torque of 95 m • N.

(b) If the six-sided bolt head is 15 mm across (Fig. 10–55), estimate the force applied near each of the six points by a wrench.

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(II) An engineer estimates that under the most adverse expected weather conditions, the total force on the highway sign in Fig. 11–33 will be F→ = (± 2.4 î - 4.1 ĵ) kN, acting at the cm. What torque does this force exert about the base O?

A particle of mass m uniformly accelerates as it moves counterclockwise along the circumference of a circle of radius R:

r→ = î R cos θ + ĵ R sin θ

with θ = ω₀t + (1/2)αt² , where the constants ω₀ and α are the initial angular velocity and angular acceleration, respectively. Determine the object’s tangential acceleration a→_tan and determine the torque acting on the object using

(a) τ→=r→×F

(II) The origin of a coordinate system is at the center of a wheel which rotates in the xy plane about its axle which is the z axis. A force F = 215 N acts in the xy plane, at a 28.0° angle to the x axis, at the point x = 28.0 cm, y = 33.5 cm. Determine the magnitude and direction of the torque produced by this force about the axis.