Acceleration in Uniform Circular Motion

Relation between angular acceleration and linear acceleration.

The speed of a particle in a circle is $2 \mathrm{m} {\mathrm{s}}^{-1}$ along the circumference of a circle of radius $0.5 \mathrm{m}$ If the speed increases at the rate of $6 \mathrm{m} {\mathrm{s}}^{-2}$. The acceleration of the particle at a given instant  is 

The magnitude of rate of change of acceleration in a uniform circular motion of angular frequency $\omega$ and radius $R$ is given by

In $7\mathrm{s}$ a car accelerates uniformly form rest to such a speed that its wheels are turning at a rate of $6 r\omega /s$. How many revolutions does the wheel turn?

A particle, starting from the position ($5 \mathrm{m},0 \mathrm{m}$), is moving along a circular path about the origin in $x-y$ plane. The angular position of the particle is a function of time as given here, $\theta =t^2+0.2t+1$. Find tangential acceleration in $\mathrm{m} {\mathrm{s}}^{-2}$

The relation between angular acceleration and tangential acceleration is given as

Define angular acceleration.

A particle is moving in a circle with constant tangential acceleration. Which one of the following is constant?

Assertion: If two different axes are at same distance from centre of mass of a rigid body, then moment of inertia of the given rigid body about both axes will always be same.

Reason: A thin uniform rod is undergoing fixed axis rotation about one of its ends with variable angular acceleration. Then, the acceleration vector of any two moving points on the rod cannot be parallel at an instant of time.

Which one is the correct relation between angular acceleration $\alpha$ and tangential acceleration $a_t$ when a particle is moving along a circular path of radius $R$.

Which one is the correct relation between angular acceleration $\alpha$ and tangential acceleration $a_t$ when a particle is moving along a circular path of radius $R$.

A mass $\mathrm{m}$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $\mathrm{m}$ and radius $R.$ Assuming pulley to be perfect uniform circular disc, the acceleration of the mass $\mathrm{m},$ if the string does not slip on the pulley is

A uniform disc of radius $20 \mathrm{cm}$ and mass $2 \mathrm{kg}$ can rotate about a fixed axis through the centre and perpendicular to its plane. A massless cord is round along the rim of the disc. If a uniform force of $2 \mathrm{newtons}$ is applied on the cord, tangential acceleration of a point on the rim of the disc will be

The linear and angular acceleration of a particle are $10 \mathrm{m} {\mathrm{s}}^{-2}$ and $5 \mathrm{rad} {\mathrm{s}}^{-2}$ respectively. It will be at a distance from the axis of rotation of-

A particle is moving in a circle with constant tangential acceleration. Which one of the following is constant?

What is the resultant acceleration of a car travelling with linear velocity $v$ on a circular road of radius $r$ that increases its speed at the rate of $a$ $\mathrm{m} {\mathrm{s}}^{-2}$ ?

A clock has a minute hand of length $8.6 \mathrm{m}$ and an hour hand of $5.4 \mathrm{m}$. What is the ratio of centripetal acceleration of a point on the tip of the minute hand to a point on the tip of the hour hand?

A uniform rod of length $l$ and mass $m$ is suspended by two vertical inextensible string as shown in figure. Then tension in the left string when right string snaps, is

A Particle is moving in a circle of radius R in such a way that at any instant the normal and tangential component of the acceleration are equal. If its speed at $\mathrm{t}=0$ is ${\mathrm{u}}_0$ , the time taken to complete the first revolution is

A particle moves in a circle of the radius $0.5 \mathrm{m}$ at a speed that uniformly increases. Find the angular acceleration of particle if its speed changes from $2.0 \mathrm{m} {\mathrm{s}}^{-1}$ to $4.0 \mathrm{m} {\mathrm{s}}^{-1}$ in $4.0 \mathrm{s}$.