Circular Motion Practice Flashcards

Comprehensive practice questions covering circular motion kinematics, dynamics, banking of roads, and various JEE Main level problems.

When a stone tied to a string is rotated in a circle and the string suddenly breaks, in which direction does the stone move?

The stone will move along a tangent to the circular path.

For a particle moving in a circle with uniform speed, which of the following is true regarding its velocity and acceleration?

Both its velocity and acceleration change because their directions are constantly changing.

If two cars of masses $m_1$ and $m_2$ move in circles of radii $r_1$ and $r_2$ and complete their circles in equal time, what is the ratio of their angular speeds $\omega_1/\omega_2$?

The ratio is $1$, because angular speed is defined as $\omega = \frac{2\pi}{T}$, and the time period $T$ is the same for both.

What is the formula for the radius of curvature of a projectile path at its highest position, given initial speed $u$ and angle $\theta$?

$$R = \frac{u^2 \cos^2(\theta)}{g}$$

A coin is placed on a rotating turntable at a distance $r$ from the center. If the coefficient of static friction is $\mu$, what is the maximum angular velocity $\omega$ the disc can have so the coin does not slip?

$$\omega = \sqrt{\frac{\mu g}{r}}$$

A coin just slips at a distance of $1\,cm$ from the center of a rotating table. If the angular velocity of the table is halved, at what distance from the center will it just slip?

$$4\,cm$$

What is the required banking angle $\theta$ for a road of radius $R$ so that a vehicle can negotiate a turn at speed $v$ without depending on friction?

$$\tan(\theta) = \frac{v^2}{Rg}$$

A bob is suspended from the roof of a car moving with constant speed $v$ in a circular track of radius $R$. What is the angle $\theta$ the massless string makes with the vertical?

$$\theta = \tan^{-1}\left(\frac{v^2}{Rg}\right)$$

For a particle of mass $m$ moving in a circular path of constant radius $r$ where centripetal acceleration varies as $a_c = k^2 r t^2$, what is the power delivered to the particle?

$$P = mk^2 r^2 t$$

If a particle moves along the circumference of a circle of radius $R$ under a central force $F$ where $F \propto \frac{1}{R^3}$, how is the time period of revolution $T$ related to the radius?

$$T \propto R^2$$

A particle of mass $m$ is attached to a spring with force constant $k$ and unstretched length $l$, rotating with angular speed $\omega$ in gravity-free space. What is the stretch in the spring?

$$x = \frac{ml\omega^2}{k - m\omega^2}$$

What is the tension in a pendulum string of length $L$ and mass $m$ at the lowest point of its path if its speed at that point is $v$?

$$T = mg + \frac{mv^2}{L}$$

A particle moves in a circle of radius $1.0\,cm$ at a speed given by $v = 2.0t\,cm/s$. What is the radial acceleration at $t = 1\,s$?

$$4.0\,cm/s^2$$

In circular motion, what does a non-zero tangential acceleration imply about the speed of the particle?

It implies that the speed of the particle is changing over time.

Calculate the centripetal force acting on a vehicle of mass $200\,kg$ moving on a curved road of radius $70\,m$ with an angular velocity of $0.2\,rad/s$.

$560\,N$ (Calculated as $F = m \omega^2 R = 200 \times (0.2)^2 \times 70$)