Embibe Experts Solutions for Chapter: Circular Motion, Exercise 3: Exercise-3

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 $\left(6\hat{i}-8\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-2}$. Find the magnitude of angular acceleration in $\mathrm{rad} {\mathrm{s}}^{-2}$. Radius of the ring is $2 \mathrm{m}$.

A particle is performing circular motion of radius $1 \mathrm{m}$. Its speed is $v=\left(2t^2\right) \mathrm{m} {\mathrm{s}}^{-1}$. What will be magnitude of its acceleration in $\mathrm{m} {\mathrm{s}}^{-2}$ at $t=1 \mathrm{s}$.

A particle moves clockwise in a circle of radius $1 \mathrm{m}$ with centre at $\left(x,y\right)=\left(1\mathrm{m},0\right)$. It starts at rest at the origin at time $t=0$. Its speed increases at the constant rate of $\left(\frac{\pi }{2}\right) \mathrm{m} {\mathrm{s}}^{-2}$. How long does it take to travel halfway around the circle in second?

Figure shows the total acceleration and velocity of a particle moving clockwise in a circle of radius $2.5 \mathrm{m}$ at a given instant of time. At this instant. Find the radial acceleration in $\mathrm{m} {\mathrm{s}}^{-2}$.

A mass $m$ rotating freely in a horizontal circle of radius $1\mathrm{m}$ on a frictionless smooth table supports a stationary mass $2\mathrm{m}$, attached to the other end of the string passing through smooth hole $O$ in table, hanging vertically. Find the angular velocity of rotation.

A circular platform rotates around a vertical axis with angular velocity $\omega =10 {\mathrm{rads}}^{-1}$. On the platform is a ball of mass $1\mathrm{kg}$, attached to the long axis of the platform by a thin rod of length $10\mathrm{cm}$ $\left(\alpha =30°\right)$. Find normal force exerted by the ball on the platform (in newton). Friction is absent.

An aircraft executive a horizontal loop at a speed of $720{\mathrm{kmh}}^{-1}$ with its wings banked at $15°$. What is the radius of the loop?

A particle of mass $3\mathrm{kg}$ is rotating in a circle of radius $1\mathrm{m}$ such that the angle rotated by its radius is given by $\theta =3\left(t+\sin t\right)$. If the net force acting on the particle when $t=\frac{\pi }{2}$ is $F$, then the find the value of $\sqrt{10}F$ in $N$.