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A small block lies on a horizontal disk at a distance $r = 0.2$ m from the axis of rotation (see the figure). The coefficient of friction between the block and the disk is $\mu = 0.5$. The disk is spun up slowly. At what angular velocity $\omega$ will the block start to slip? Find the corresponding…
A ball of mass $m = 0.1$ kg hangs on a thread of length $l = 1$ m and moves uniformly in a circle in a horizontal plane. The thread makes an angle $\alpha = 60°$ with the vertical (see the figure). Find the tension $T$ in the thread and the period $\tau$ of the ball's revolution. Take $g = 10$ m/s².
A car of mass $m = 1$ t moves at a speed $v = 36$ km/h over a convex bridge of radius of curvature $R = 40$ m (see the figure). With what force does the car press on the bridge at its highest point? At what speed will the car stop pressing on the bridge at the top (lose contact with it)? Take …
A satellite moves in a circular orbit around the Earth of radius $r = 10000$ km. The acceleration due to gravity in this orbit is $g \approx 4$ m/s². Find the linear speed of the satellite.
A disk rotates around a circle of radius $r = 0.5$ m with frequency $f = 2$ Hz. Find the centripetal acceleration of a point on the edge of the disk.
A car goes through a turn of radius $r = 50$ m at a speed of $v = 72$ km/h. Find the centripetal acceleration of the car.
A car of mass m = 1000 kg moves in a horizontal circle of radius r = 50 m at a speed of v = 10 m/s. Find the centripetal acceleration of the car and the force acting on it.