Angular Variables

A particle completes 2 revolutions in a circular path of radius 3 cm. The angular displacement of the particle will be (in radian)

A particle is performing U.C.M. along a circle of radius $R$. In half the period of revolution, its displacement and distance covered are respectively

A particle moves along a circular path of radius '$r$' with uniform speed '$v$'. The angle described by the particle in two seconds in radians is

Two particles having mass 'M' and 'm' are moving in a circular path with radius 'R' and 'r' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to that of the second particle will be

A body moves along a circular path of diameter $30$ cm. It starts from one end of diameter, moves along the circular path and reaches the other end of diameter in 3 second. The angular speed of the body in radian per second is

Angular velocity of hour hand of a watch is (in rad/s)

The difference between angular speed of minute hand and second hand of a clock is (in rad/s)

The relative angular speed of hour hand and minute hand of clock is

The angular speed of the minute hand of a clock in degrees per second is

A particle performing U.C.M. of radius $\frac{\pi}{2}$ m makes 'x' revolutions in time t. Its tangential velocity is

Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speeds $v_A$ and $v_B$ respectively. $T_A$ and $T_B$ are the time periods of rotation of the particles respectively and their relation is $T_A = 3T_B$. The ratio of angular speed of B to that of A will be

The position vector of a particle is $\vec{r} = a\cos\omega t\,\hat{i} + a\sin\omega t\,\hat{j}$. Calculate the angle between its position vector and the velocity vector.

($\cos 0 = 1, \cos 90 = 0, \cos 60 = 0.5, \sin 30 = 0.5, \sin 0 = 0$)

A sportsman runs around a circular track of radius $r$ such that he traverses the path $ABAB$. The distance travelled and displacement, respectively, are

A particle performing uniform circular motion of radius $\frac{\pi}{2}\text{ m}$ makes $x$ revolutions in time $t$. Its tangential velocity is

A cyclist starts from the point $P$ of a circular ground of radius $2\text{ km}$ and travels along its circumference to the point $S$. The displacement of a cyclist is:

A body moves along a circular path of radius 15 cm. It starts from a point on the circular path and reaches the end of diameter in 3 seconds. The angular speed of the body in $\text{rad/s}$ is

Two objects of masses ' $m_1$ ' and ' $m_2$ ' are moving in the circles of radii ' $r_1$ ' and ' $r_2$ ' respectively. Their respective angular speeds ' $\omega_1$ ' and ' $\omega_2$ ' are such that they both complete one revolution in the same time ' $t$ '. The ratio of linear speed of ' $m_2$ ' to that of ' $m_1$ ' is

A clock has $75\text{ cm}, 60\text{ cm}$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi = 3.14$):

The linear speed of a particle at the equator of the earth due to its spin motion is ' V '. The linear speed of the particle at latitude $30^\circ$ is

$\left[\begin{matrix} \sin 30^\circ = \cos 60^\circ = 1/2 \\ \cos 30^\circ = \sin 60^\circ = \sqrt{3}/2 \end{matrix}\right]$

A wheel of radius 1 m rolls through $180^\circ$ over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is.

Two particles having mass '$M$' and '$m$' are moving in a circular path with radius '$R$' and '$r$' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second particle will be

A particle performing uniform circular motion of radius $\frac{\pi}{2}\text{ m}$ makes '$x$' revolutions in time '$t$'. Its tangential velocity is

A body is moving with constant speed, in a circle of radius $10\text{ m}$. The body completes one revolution in $4\text{ s}$. At the end of 3rd second, the displacement of body (in $\text{m}$) from its starting point is:

A particle moves around a circular path of radius '$r$' with uniform speed '$V$'. After moving half the circle, the average acceleration of the particle is

A particle is moving in a circle with uniform speed '$v$'. In moving from a point to another diametrically opposite point

As shown in the figure, a particle is moving with constant speed $\pi\text{ m/s}$. Considering its motion from $A$ to $B$, the magnitude of the average velocity is:

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^\circ$, the ratio of instantaneous velocity to its average velocity is $\pi : x\sqrt{2}$. The value of $x$ will be -

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is $60\text{ m}$, then the magnitude of displacement would be:

(Given $\cos 135^\circ = -0.7)$

A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms${}^{-1}$. (take $\pi$ = 3.14)

The angular displacement of body performing circular motion is given by $\theta = 5\sin\frac{\pi t}{6}$. The angular velocity of the body at $t = 3$ second will be $\left[\sin\frac{\pi}{2} = 1, \cos\frac{\pi}{2} = 0\right]$

If $\omega_1$ is angular velocity of hour hand of clock and $\omega_2$ is angular velocity of the earth, then the ratio $\omega_1$: $\omega_2$ is

A huge circular arc of length 4.4 ly subtends an angle of 4″ (4 seconds of arc) at the centre of the circle. How long it would take for a body to complete 4 revolutions if its speed is 8 AU per second? Given: 1 ly = 9.46 $\times$ 1015 m

1 AU = 1.5 $\times$ 1011 m

A particle is moving in a radius $R$ with constant speed $v$. The magnitude of average acceleration after half revolution is

A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60o around the centre of the circle?

In U.C.M., when time interval $\delta t \to 0$, the angle between change in velocity ( $\delta \vec{v}$) and linear velocity $(\vec{v})$ will be