Circular Motion

A particle is moving uniformly on a horizontal circular path. Work done by centripetal force on the particle in one half revolution is

A weightless thread can withstand tension upto $30 \mathrm{N}$. A stone of mass $0.5 \mathrm{kg}$ is tied to it and is revolved in a circular path of radius $2 \mathrm{m}$ in a vertical plane .If $g=10 \mathrm{m}/{\mathrm{s}}^2$, the maximum angular velocity of the stone can be?

A cyclist is moving on a circular path with constant speed $v$. What is the change in its velocity after it has described an angle of $30°$.

A car travels on a banked horizontal road with inclination $45°$. What is its maximum speed for not skidding up $\left(\mu =0.75,R=200\right)$.

Why a cyclist lean inwards when negotiating a curve?

Why out side of road is raised at the turning? 

Obtain an expression for the maximum speed with which a vehicle can safely negotiate a curved rough road banked at an  angle $\theta$.

A car is moving on a circular road of radius $150 \mathrm{m}$ with a coefficient of friction $0.6$. With what optimum velocity should the car be moved so that it crosses the turn safely.:

A circular track of radius $400 \mathrm{m}$ is banked at an angle of$10°$ . If the coefficient of friction between the tyre of a car and the track is $0.2$, what is the,

(a) optimum speed of the car to avoid the wear and tear on its tyre, and 

(b) Maximum permissible speed to avoid slipping.

What is the minimum speed a car can travel on an inclined road in terms of radius of the curved path $R$, acceleration due to gravity $g$, coefficient of static friction ${\mu }_s$, and the inclined angle of the road?

When moving on an circular inclined road slowly, friction prevents the vehicle from sliding inside the circular path.

When a car is moving in minimum speed on an inclined path, what will be the direction of friction between the wheels and the road?

Derive the formula of minimum safe speed of a vehicle moving on an inclined circular track.

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

A circular race course track has a radius of$500 \mathrm{m}$ and is banked to $10°$. If the coefficient of friction between tyres of vehicle and the road surface is $0.25$. Compute the optimum speed to avoid wear and tear of tyres, ($g = 9.8 \mathrm{m}/{\mathrm{s}}^2$).
 

A circular race course track has a radius of$500 \mathrm{m}$ and is banked to $10°$. If the coefficient of friction between tyres of vehicle and the road surface is $0.25$. Compute the maximum speed to avoid slipping.
 

A motor van weighing $4400 \mathrm{kg}$ rounds a level curve of radius $200 \mathrm{m}$ on un-banked road at $60 \mathrm{km}/\mathrm{hr}$. What should be the minimum value of coefficient of friction to prevent skidding? At what angle the road should be banked for this velocity?
 

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?

Show that the angle of banking is independent of mass of vehicle.

Obtain an expression for maximum safety speed with which vehicle can be safely driven along curved banked road.