14. Torque & Rotational Dynamics

In FIGURE EX12.19, for what value of X_axle will the two forces provide 1.8 Nm of torque about the axle?

(II) The bolts on the cylinder head of an engine require tightening to a torque of 95 m N. If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?

The bolts on the cylinder head of an engine require tightening to a torque of 95 m-N. 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.

An engineer estimates that under the most adverse expected weather conditions, the total force on the highway sign in Fig. 11–33 will be $\overrightarrow{F}$ = (± 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: $\overrightarrow{r}$ = 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 $\overrightarrow{a}$_tan and determine the torque acting on the object using $\overrightarrow{\tau }=\overrightarrow{r}\times F$.

(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.