Uniform 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  $\frac{3\mathrm{R}}{4}$ 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. The normal reaction on the ring by the track is

A hemispherical bowl of radius $R=0.1 \mathrm{m}$ is rotating about its own axis (which is vertical), with an angular velocity $\omega$. A particle of mass ${10}^{-2} \mathrm{kg}$ on the frictionless inner surface of the bowl is also rotating with the same $\omega$. The particle is at a height $h$ from the bottom of the bowl.
Obtain the relation between $h$ and $\omega$. What is the minimum value of $\omega$ needed, in order to have a non-zero value of $h$ ?

An electric line of force in the $x-y$ plane is given by the equation $x^2+y^2=1$. A particle with unit positive charge, initially at rest at the point $x=1,y=0$ in the $x-y$ plane, will move along the circular line of force.

Why is centrifugal force considered as an imaginary force?

In circular motion speed depends on angular position as $v= \left(\theta +5\right) \mathrm{m}/\mathrm{s}$. The value of $\theta$ as a function of time $t$ is

An artificial satellite is orbiting around the earth with the speed of $4 \mathrm{km} {\mathrm{s}}^{-1}$  at a distance of ${10}^4 \mathrm{km}$ from the earth. Calculate its centripetal acceleration. 

 A stone tied to the end of the string $100 \mathrm{cm}$ long is whirled in a horizontal circle with a constant speed.If the stone makes $30$ revolutions in $15 \mathrm{s}$. Calculate the magnitude and direction of the acceleration of the stone. 

An aircraft executes a horizontal loop of radius $1 \mathrm{km}$ with a steady speed of $900 \mathrm{km} {\mathrm{h}}^{-1}$.  Compare its centripetal acceleration with the acceleration due to gravity? 

 A stone is tied at the end of a string $1 \mathrm{m}$ long and whirled round by holding the other end.  The stone makes $120$ revolutions in $12 \mathrm{seconds}$. Calculate its angular velocity and linear velocity.

The angular displacement of a body is given by $\theta =2t^2+5t-3$. Find the value of the angular velocity and angular acceleration when $t=2s$.

Derive an equation for the angle covered by a rotating rigid body in the nth second.Enable GingerCannot connect to Ginger Check your internet connection
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The blades of an aeroplane propeller are $2 \mathrm{m}$ long and rotate at $300 \mathrm{rpm}$.  Calculate linear velocity of a point on the aeroplane blade, $0.5 \mathrm{m}$ from the axis of rotation.

The blades of an aeroplane propeller are $2 \mathrm{m}$ long and rotate at $300 \mathrm{rpm}$.  Calculate angular velocity of a point on the blade, $0.5 \mathrm{m}$ from the axis of rotation.

The blades of an aeroplane propeller are $2 \mathrm{m}$ long and rotate at $300 \mathrm{rpm}$. Calculate the period of rotation of a point on a lade, $0.5 \mathrm{m}$ from the axis of rotation.

The blades of an aeroplane propeller are $2 \mathrm{m}$ long and rotate at $300 \mathrm{rpm}$.  Calculate frequency of a point on a blade, $0.5 \mathrm{m}$ from the axis of rotation of the blades.

What is the angular velocity of a body on the surface of the earth at the equator ? Also find its linear velocity. Given radius of the earth is $6400 \mathrm{km}$. Period of rotation of the earth is $24 \mathrm{hours}$.

What is the angular velocity of a minute hand of a clock?

What is the angular velocity of a second hand of a clock?