Two particles each of mass $m$ are moving in horizontal circle with same angular speed. If both string are of same length then the ratio of tension in string $\frac{T_1}{T_2}$ is .........

A particle moves so that its position vector is given by $\overrightarrow {\;r} = cos\omega t\,\hat x + sin\omega t\,\hat y$ , where $\omega$ is a constant.  Which of the following is true?  

The angular acceleration of a body, moving along the circumference of a circle, is :

A man is running with constant speed along a circular path of radius $2 \sqrt 2\, m$. He completes $1$ round in $10\, second$. Find instantaneous speed at $2.5 \,sec.$

A cyclist is riding with a speed of $27 \;km/h.$ As he approaches a circular turn on the road of radius $80\; m$, he applies brakes and reduces his speed at the constant rate of $0.50\; m/s$ every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?

A particle is moving on a circular path of radius $r$ with uniform speed $v$. The magnitude of change in velocity when the particle moves from $P$ to $Q$ is  $(\angle POQ = 40^o)$