Motion in a Vertical Circle

A small sphere is attached to a cord and rotates in a vertical circle about a point $O$. If the range speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at:

A stone tied to a string is rotated in a vertical circle. The minimum speed of the stone during a complete vertical circular motion 

A smooth semicircular wire track of radius $R$ is fixed in a vertical plane One end of a massless spring of natural length  $\frac{\mathrm{}\mathrm{}\mathrm{}3R}{4}$  is attached to the lowest point $O$of the wire track. A small ring of mass $m$ which can slide on the track is attached to the other end of the spring. The ring is held stationary at point $P$ such that the spring makes an angle of  $60°$ with the vertical. The spring constant $K=\frac{mg}{R}$ . Consider the instant when the ring is released. Find the normal reaction on the ring by the track.

When does the body oscillates about the lowest point in vertical circle?

A ball of mass $\text{20kg}$ is suspended from a massless string of length$5\mathrm{m}.$.A bullet of mass $5\mathrm{kg}$moving with velocity $v_0 m/s$ collides with the ball and sticks to it. Find the minimum value of ${\mathrm{v}}_0$ so that the combined mass completes the vertical circular motion.

There is a rod of length l and mass m. It is hinged at one end to the ceiling. The time period of small oscillation is

A simple pendulum, composed of a bob of mass m connected to the end of a massless rod, executes simple harmonic motion as it swings through small angles of oscillation.Which of the following would enable you to calculate the length of the pendulum?

An iron ball and an aluminium ball of different radius are released from a height h in vaccum.What is the time taken by both of them to reach the ground?

Discuss the motion in vertical circle.

Minimum velocity required to complete vertical circle of radius$\mathrm{R}$ at lowest point is $\sqrt{5\mathrm{gR}}$.

A pendulum string of length $𝓁$ moves up to a horizontal position as shown in figure and released.




What should be the minimum strength of the string to withstand the tension as the pendulum passes through the position of equilibrium? The mass of the pendulum is $m$.

There is a parabolic bridge across a river of width $10 \mathrm{m}$. The highest point of the bridge is $4 \mathrm{m}$ above the level of the bank. A car of mass $72 \mathrm{kg}$ is crossing the bridge at a constant speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$. Find the force (in Newton) exerted on the bridge by the car when it is at the highest point $P$ of the bridge in newton. (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

A particle is tied to a string describes a vertical circular motion of radius $r$ continually. If it has a velocity $\sqrt{3gr}$ at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If radius of the disc is $1 \mathrm{m}$ then the distance (in meter) travelled by $P$ in one full rotation of the disc is

The velocity of a body, undergoing motion in a vertical circle is maximum at _____ .
(Choose from: top/bottom)

A ball is released from height along the slope and move along a circular track of radius $R$ without falling vertically downwards. Show that $h=\frac{5}{2}R$.

An object of mass $0.5 \mathrm{kg}$ attached to a string of length $0.5 \mathrm{m}$ is whirled in a vertical circle at constant angular speed. If the maximum tension in the string is $5 \mathrm{kg}$ wt, calculate maximum number of revolutions it can complete in a minute.

An object of mass $0.5 \mathrm{kg}$ attached to a string of length $0.5 \mathrm{m}$ is whirled in a vertical circle at constant angular speed. If the maximum tension in the string is $5 \mathrm{kg} \mathrm{wt}$, calculate speed of object.

A stone weighing $1 \mathrm{kg}$ is whirled in a vertical circle attached at the end of a rope of length $0.5 \mathrm{m}$. Find the tension at highest position.