Force F = ─10ĵ N is exerted on a particle at 𝓇 = (5î＋5ĵ) m. What is the torque on the particle about the origin?

(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?