Rotational and Circular Motion

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by t, lying in the interval 0 to 2p, is associated with the maximum translation of the follower during one full rotation of the cam rotating about the center at (x, y) = (0, 0)?

A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity $\omega$ and angular acceleration $\alpha$. The magnitude of the acceleration of the point of contact on the disc is

In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is

In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and the thickness 8 mm undergoes 10% reduction of thickness. The angle of bite (in radians) is

A circular object of radius r rolls without slipping on a horizontal level floor with the centre having velocity V. The velocity at the point of contact between the object and the floor is

For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD (in rad/s) is

A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

The rotor shaft of a large electric motor supported between short bearings at both deflection of 1.8 mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is

A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L/3 from the hinge so that the rod swings to the right. The reaction at the hinge is

A straight rod of length L(T), hinged at one end and freely extensible at the other end, rotates through an angle $\theta$(t) about the hinge. At time t, L(t) = 1 m, L(t) = 1 m/s, $\theta$(t) = $\frac{\pi}{4}$ rad and $\theta$(t) = 1 rad/s The magnitude of the velocity at the other end of the rod is

A circular disk of radius R rolls without slipping at a velocity $v$. The magnitude of the velocity at point P (see figure) is