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Chapter 11: Problem 1
Does Earth's angular velocity vector point north or south?
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You slip a wrench over a bolt. Taking the origin at the bolt, the other end of the wrench is at \(x=18 \mathrm{cm}, y=5.5 \mathrm{cm} .\) You apply a force \(\vec{F}=88 \hat{\imath}-23 \hat{\jmath} \mathrm{N}\) to the end of the wrench. What's the torque on the bolt?
A time-dependent torque given by \(\tau=a+b \sin c t\) is applied to an object that's initially stationary but is free to rotate. Here \(a, b\) and \(c\) are constants. Find an expression for the object's angular momentum as a function of time, assuming the torque is first applied at \(t=0\).
As an automotive engineer, you're charged with redesigning a car's wheels with the goal of decreasing each wheel's angular momentum by \(30 \%\) for a given linear speed of the car. Other design considerations require that the wheel diameter go from \(38 \mathrm{cm}\) to \(35 \mathrm{cm} .\) If the old wheel had rotational inertia \(0.32 \mathrm{kg} \cdot \mathrm{m}^{2},\) what do you specify for the new rotational inertia?
A \(12-\mathrm{N}\) force is applied at the point \(x=3 \mathrm{m}, y=1 \mathrm{m} .\) Find the torque about the origin if the force points in (a) the \(x\) -direction, (b) the \(y\) -direction, and (c) the \(z\) -direction.
Vector \(\vec{A}\) points \(30^{\circ}\) counterclockwise from the \(x\) -axis. Vector \(\vec{B}\) has twice the magnitude of \(\vec{A}\). Their product \(\vec{A} \times \vec{B}\) has magnitude \(A^{2}\) and points in the negative \(z\) -direction. What's the direction of vector \(\vec{B} ?\)
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