Centripetal and Centrifugal Forces

Derive an expression for the maximum speed of a vehicle along a curved path.

An astronaut is orbiting the earth in a Space Station. Draw diagram to show the force exerted by the Earth on the astronaut and on the Space Station. Include the Earth on your diagram. Label each Arrow with the name of the force.

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

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 moves along an uneven horizontal surface with a constant speed at all points. The normal reaction of the road on the car is

A particle of mass $2 \mathrm{kg}$ suspended with the help of sa tring of length $0.72 \mathrm{m}$ is given velocity of $v_0=6 \mathrm{m} {\mathrm{s}}^{-1}$ at its lowest position. Tension in the string at its lowest position is $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A mass of $3 \mathrm{kg}$ is whirled in a horizontal circle by means of a string with initial speed of $6$ r.p.m. Keeping the radius constant the tension in the string becomes $4$ times. Then the new speed will be

In figure, as the van moves at constant speed from point $A$ to point $B$, the weight of a passenger recorded by a platform scale changes from $600 \mathrm{N}$ to $400 \mathrm{N}$. The speed of the van is close to

A long playing record revolves with a speed of $33\frac{1}{4}$ rev/min. and has a radius of $15 \mathrm{cm}$.  Two coins are placed at $4 \mathrm{cm}$ and  $14 \mathrm{cm}$ away from the centre of the record. If the coefficients of friction between the coin and the record is $0.15$, which of the two coins will revolve with record ?

A body of mass $0.5 \mathrm{kg}$ is whirled with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$ using $0.5 \mathrm{m}$ length string which can withstand a tension of $15 \mathrm{N}$.  Neglecting the force of gravity on the body predict whether the string will break or not.

Which region of the earth experiences maximum centripetal force ?

A pilot does not fall down when his aeroplane loops the loop. Why ?

What provides the centripetal force to a car taking a turn on a level road ?

A cyclist wants to loop the loop inside the death globe of diameter $5m$. Find the minimum velocity, that he should have at the lowest point and calculate the height from which he should start it .

What is the work done by the centripetal force?

A circular disc rotates at $60$ revolutions per minute about an axis passing through its center. A coin of $18 \mathrm{g}$ is placed at a distance of $8 \mathrm{cm}$ from the center of the disc. The centrifugal force on the coin is

When a body moves with a constant speed along a circle

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 $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$