Dynamics of Circular Motion

List three real life examples of circular motion

Explain the reason behind the bending of cyclist on a horizontal road while taking a turn.

A vehicle is moving on a horizontal circular track of radius $\mathrm{r}$, the distance between the wheels is $\mathrm{d}$, the height of centre of gravity of vehicle is $\mathrm{h}$ from the ground. The vehicle will overturn if its velocity is:-

A designer of racetrack is appointed on moon for a car race. He has to design a $1.5 \mathrm{km}$ diameter circular racetrack assuming a speed of $240 \mathrm{km}/\mathrm{hr}$ for the type of cars used. If everything else is to stay the same in the design, by how many degrees with respect to the horizontal, designers will have to change the angle at which the track is banked on the moon as compared to the banking angle on earth ? The acceleration of gravity on the moon is $1.62 \mathrm{m}/{\mathrm{s}}^2$.

A person applies a constant horizontal force $\overrightarrow{\mathrm{F}}$on a particle of mass $\mathrm{m}$ and finds that the particle move in a circle of the radius $\mathrm{r}$ with a uniform speed $\mathrm{v}$. To maintain the uniform circular motion, select the correct option-

A particle initially at rest starts moving from point $\mathrm{A}$ on the surface of a fixed frictionless hemisphere of radius $\mathrm{r}$ as shown in the figure. The particle loses its contact with a hemisphere at point $\mathrm{B}$ and point $\mathrm{C}$ is center of the hemisphere, then select the equation which gives the relation between $\alpha$ and $\beta$-

A particle of mass $\mathrm{m}$ is revolving along a circular path of constant radius $r$ in such a way that its centripetal acceleration $a_r$ is changing with time $t$ according to the equation $a_r=k^{2}r{t}^2$ where $k$ is constant. The power exerted by the force acting on the particle is

A particle of mass $\mathrm{m}$ is tied to one end of a string of length $l$ and rotated though the other end along a horizontal circular path with speed $v$. The work done in full horizontal circle is

A car is moving in a circular horizontal track of radius $10 \mathrm{m}$ with constant speed of $10 \mathrm{m}/\mathrm{s}$. A plumb bob is suspended from the roof of the car by a light rigid rod. The angle made by the rod with the vertical is $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$

A motor car is moving with a speed of $30 \mathrm{m}/\mathrm{s}$ on a circular track of radius $500 \mathrm{m}$. Its speed is increasing at the rate of $2 \mathrm{m}/{\mathrm{s}}^2$. What will be its resultant acceleration?

A particle of mass $\mathrm{m}$ is revolving along a circular path of constant radius $r$ in such a way that its centripetal acceleration $a_r$ is changing with time $t$ according to the equation $a_r=k^{2}r{t}^2$ where $k$ is constant. The power exerted by the force acting on the particle is

A stone, tied at one end of rope, is whirled along a horizontal circle with great speed. Suddenly the rope snaps. In which direction will the stone fly off?

When a particle is made to rotate with uniform velocity in a circular path, in which direction is its acceleration directed?

A bottle of soda lime grasped by the neck and swung briskly in a vertical circle. Near which portion of the bottle do the bubbles collect ?

A car of mass m is taking a circular turn of radius $\mathrm{r}$ on a frictional level road with a speed $\vartheta$. In order that the car does not skid 

In a circus, a motor cyclist rides in circular track of radius $\text{'}\mathrm{r}\text{'}$ in the vertical plane. The minimum velocity at the highest point of the track will be

A rod of length $L$ is pivoted at one end and is rotated with a uniform angular velocity, in a horizontal plane. Let $T_1$ and $T_2$ be the tensions at points $\frac{L}{4}$ and $\frac{3L}{4}$, away from the pivoted ends.

A particle when moves in a circle with a uniform speed:

A motor cyclist at a speed of $5 \mathrm{m}/\mathrm{s}$ is describing a circle of radius $25 \mathrm{m}$. Find his inclination with vertical. What is the value of coefficient of friction between tyre and ground?

What is banking of roads? Why is it necessary?