Show that the minimum angular speed necessary to keep a rider `omega = sqrt(g/(mu_sR)`.

A motor cyclist is to undertake horizontal circles inside the cylindrical wall of a well of inner radius 4m . Coefficient of static friction between the tyres and the wall is 0.4. Calculate the minimum speed and frequency necessary to perform this stunt.

A simple pendulam of length L carriers a bob of mass m. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal the net force on the bob is

Show that the maximum safety speed (V_max) = sqrt{(rg(mu_s+tantheta))/((1-mu_s tantheta)

A motorcyclist rides in a horizontal circle along the inner wall of cylindrical chamber of radius r. If the coefficient of friction between the tyres and the wall of is mu , the minimum angular speed to prevent him from sliding down is

A tuning fork of frequency 340 Hz is vibrated just above the tube of 120 cm height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance? (speed of sound in the air = 340m/s)

A person stands in contact against a wall of cylindrical drum of radius 'r' rotating with angular velocity omega .If mu is coefficient of static fiction between the wall and the person , then the minium rotational speed which enables the person to remain stuck to the wall will be

According to Bohr's theory the angular speed omega of electron related to n is

The mean radius of the earth is R , its angular speed on its own axis is omega and the acceleration due to gravity at earth's surface is g . The cube of the radius of the orbit of a geo-stationary satellite will be

Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed omega . The discs are in the same horizontal plane. At time t-0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is v_r , As a function of time, it is best represented by