A scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$

A solid disc rolls clockwise without slipping over a horizontal path with a constant speed $\upsilon $. Then the magnitude of the velocities of points $A, B$ and $C$ (see figure) with respect to a standing

A car is going round a circle of radius $R_1$ with constant speed. Another car is going round a circle of radius $R_2$ with constant speed. If both of them take same time to complete the circles, the ratio of their angular speeds and linear speeds will be .........

Read each statement below carefully and state, with reasons, if it is true or false :

$(a)$ The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre

$(b)$ The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

$(c)$ The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in rad/s is,:

A particle moves with constant angular velocity in a circle. During the motion its