A particle moves in uniform circular motion with radius 0.4 m and completes 3 revolutions in 2 seconds. What is the total linear distance traveled by the particle during this time?

Two solid disks have the same thickness and are made of the same material. Disk A has twice the radius of disk B. If both disks rotate with the same angular velocity about axes through their centers, what is the ratio of the rotational kinetic energy of disk A to that of disk B?

In the cross-product formula for torque $$\vec{\tau}=\vec{r} \times \vec{F}$$, what does the angle $$\theta$$ represent in the calculation of torque magnitude?

A thin uniform rod of length $$L$$ and mass $$M$$ rotates about an axis perpendicular to the rod, passing through a point at a distance $$d$$ from the rod's center. For what value of $$d$$ is the moment of inertia minimized?

A student claims that to maximize torque, one should always apply force as far from the axis of rotation as possible. Under what condition is this claim NOT valid?