Embibe Experts Solutions for Chapter: Circular Motion, Exercise 1: BEGINNER'S BOX - 1

A stone tied to the end of a $80 \mathrm{cm}$ long string is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25 \mathrm{s}$, the magnitude of its acceleration is :

For a body in a circular motion with a constant angular velocity, the magnitude of the average acceleration over a period of half a revolution is.... times the magnitude of its instantaneous acceleration.

A ring rotates about $z$ axis as shown in figure. The plane of rotation is $xy$. At a certain instant the acceleration of a particle $P$ (shown in figure) on the ring is $( 6\hat{\mathrm{i}} - 8\hat{\mathrm{j}}) {\mathrm{ms}}^{-2}$. Find the angular acceleration of the ring and its angular velocity at that instant. Radius of the ring is $2 \mathrm{m}$. 

A disc rotates about a fixed axis. Its angular velocity $\omega$ varies with time according to the equation $\omega$ $=at+b$. Initially at $t=0$ its angular velocity is $1.0 \mathrm{rad} {\mathrm{s}}^{-1}$ and angular position is $2 \mathrm{rad}$; at the instant $t=2 \mathrm{s}$, angular velocity is $5.0 \mathrm{rad} {\mathrm{s}}^{-1}.$ Determine angular position $\theta$ and angular acceleration $\alpha$ when $t=4 \mathrm{s}$.

A wheel of radius $1.5 \mathrm{m}$ is rotating at a constant angular acceleration of $10 \mathrm{rad} {\mathrm{s}}^{-2}$. Its initial angular speed is $\left(\frac{60}{\pi }\right)$ $\mathrm{rpm}$. What will be its angular speed and angular displacement at $t=2.0 \mathrm{s}$?

A car has wheels of radius $0.30 \mathrm{m}$ and is travelling at $36 \mathrm{m} {\mathrm{s}}^{-1}$. Calculate the angular speed of the wheel.

A car has wheels of radius $0.30 \mathrm{m}$ and is travelling at $36 \mathrm{m} {\mathrm{s}}^{-1}.$ Calculate if the wheels describe $40$ revolutions before coming to rest with uniform acceleration. Find its angular acceleration. 
 

A car has wheels of radius $0.30 \mathrm{m}$ and is travelling at $36 \mathrm{m} {\mathrm{s}}^{-1}$. Calculate if the wheels describe $40$ revolutions before coming to rest with a uniform acceleration the distance covered.