Non-Uniform Circular Motion

A car is travelling at 40 m/s on a circular path of radius 40 m. It is increasing its speed at the rate of $2$ m/s$^{2}$. Its net acceleration is (in m/s$^{2}$) nearly

In non uniform circular motion, the ratio of radial acceleration to tangential acceleration is (V is the velocity, r is the radius and $\alpha$ is the angular acceleration)

A particle is rotating in a circular path and at any instant its motion can be described as $\theta = \frac{5t^4}{40} - \frac{t^3}{3}$.

The angular acceleration of the particle after 10 seconds is _________ rad/s2.

A particle is moving with constant angular acceleration $4$ rad/s$^{2}$ in circular path. At what time the magnitudes of its tangential acceleration and centripetal acceleration will be equal?

A particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius 'r'. At certain instant, the magnitude of centripetal acceleration is $\left(\frac{1}{3}\right)^{rd}$ the tangential acceleration. The relation between linear speed (V) and angular acceleration ($\alpha$) is

A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first 2 s and a further angle $\theta_2$ in the next 2 s, the ratio $\theta_1 : \theta_2$ is

When a ceiling fan is switched off, its angular velocity falls to $\left(\frac{1}{3}\right)$rd while it makes 24 rotations. How many more rotations will it make before coming to rest?

A particle at rest starts moving with a constant angular acceleration of $4\text{ rad/s}^2$ in a circular path. The time at which magnitudes of its centripetal acceleration and tangential acceleration will be equal, is (in second)

A disc at rest is subjected to a uniform angular acceleration about its axis. Let $\theta$ and $\theta_1$ be the angle made by the disc in $2$nd and $3$rd second of its motion. The ratio $\frac{\theta}{\theta_1}$ is

A particle starting from rest moves along the circumference of a circle of radius ' $r$ ' with angular acceleration ' $\alpha$ '. The magnitude of the average velocity in time it completes the small angular displacement ' $\theta$ ' is

A particle is moving in a circle of radius $50\text{ cm}$ in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at $t = 0$ is $4\text{ m/s}$, the time taken to complete the first revolution will be $\frac{1}{\alpha}\left[1 - e^{-2\pi}\right]\text{ s}$, where $\alpha =$ _________.

A particle at rest starts moving with constant angular acceleration $4\text{ rad/s}^2$ in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?

A particle of mass '$m$' moves along a circle of radius '$r$' with constant tangential acceleration. If K.E. of the particle is '$E$' by the end of third revolution after beginning of the motion, then magnitude of tangential acceleration is

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $t(1 - e^{-\pi/2})\text{ s}$. The value of t is ____________.

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

A particle at rest starts moving with a constant angular acceleration of $4\text{ rad/s}^2$ in a circular path. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

A body is moving along a circular track of radius 100 m with velocity $20\text{ m/s}$. Its tangential acceleration is $3\text{ m/s}^2$, then its resultant acceleration will be

In non-uniform circular motion, the ratio of tangential to radial acceleration is ($r =$ radius, $\alpha =$ angular acceleration and $v =$ linear velocity)

A particle starting from rest moves along the circumference of a circle of radius $r$ with angular acceleration $\alpha$. The magnitude of the average velocity, in the time it completes the small angular displacement $\theta$ is

A child starts running from rest along a circular track of radius $r$ with constant tangential acceleration a. After time $t$ he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is

[g = acceleration due to gravity]

A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^3 + 5,$ where $s$ is in metres and $t$ is in seconds. The radius of the path is $20\text{ m}.$ The acceleration of $'P'$ when $t = 2\text{ s}$ is nearly.