Acceleration in Uniform Circular Motion

Relation between angular acceleration and linear acceleration.

A block of mass $M$ is released from rest on top of a smooth inclined plane of inclination$\theta$. The block is connected to a light string which is wound over a disc shaped pulley of mass $M$ and radius$R$ as shown. If length of inclined surface is $I$, then time (in second) taken by the block to reach the bottom is-------------------(given:$\frac{l}{g\sin \theta }=3, in SI units$)

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

A wheel of radius $1 \mathrm{m}$ is spinning with angular velocity which varies with time as $5 t^2 \mathrm{rad}/\mathrm{s}$. The acceleration of the point on the wheel's rim at $t=1 \mathrm{s}$, has the magnitude equal to _____.

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 $\mathrm{m} {\mathrm{s}}^{-2}$

A motor part at $1.5 \mathrm{m}$ from the motor's axis of rotation has a constant acceleration of $0.25 \raisebox{1ex}{$\mathrm{rad}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$. Find the magnitude of its linear acceleration at the instant when its angular speed is $0.5 \raisebox{1ex}{$\mathrm{rad}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$

Establish the relation between angular acceleration and linear acceleration.

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?

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 $R$.

Define angular acceleration and translational acceleration.

A particle is moving along a circular path of radius $2 \mathrm{m}$ with a tangential acceleration of $10 \mathrm{m} {\mathrm{s}}^{-2}$. Calculate its angular acceleration.

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 $R$.

Obtain the relation between magnitude of linear acceleration and angular acceleration in circular motion.

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 body is moving along a circle at a constant speed of $10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$, then choose the relation between acceleration and radius.