Dynamics of Circular Motion

A circular disc with a groove along its diameter is placed horizontally on a rough surface. A block of mass $1 \mathrm{kg}$ is placed as shown. The co-efficient of friction between the block and all surfaces of groove and horizontal surface in contact is $\mu =\frac{2}{5}.$ The disc has an acceleration of $25 {\mathrm{ms}}^{-2}$ towards left. Find the acceleration of the block with respect to disc. Given, $\cos \theta =\frac{4}{5}, \sin \theta =\frac{3}{5}$

Two blocks of mass $m_1=10 \mathrm{kg}$ and $m_2=5 \mathrm{kg}$, connected to each other by a massless inextensible string of length $0.3 \mathrm{m}$ are placed along a diameter of a turn table. The coefficient of friction between the table and $m_1$ is $0.5$ while there is no friction between $m_2$ and the table. The table is rotating with an angular velocity of $10 {\mathrm{rads}}^{-1}$ about a vertical axis passing through its centre $O$. The masses are placed along the diameter of the table on either side of the centre $O$ such that the mass $m_1$ is at a distance of $0.124 \mathrm{m}$ from $O$. The masses are observed to be at rest with respect to an observer on the turn table. Calculate the frictional force on $m_1$.

A disc revolves with a speed of $120$ $\mathrm{rev}./\min .$ and has a radius of $15 \mathrm{cm}.$ Two coins $\mathrm{A}$ and $\mathrm{B}$ are placed at $4 \mathrm{cm}$ and $14 \mathrm{cm}$ away from the centre of the record. If the coefficient of friction between the coins and the record is $0.16.$ which of the coins will revolve with the record ?

A cabin is moving vertically upwards with an acceleration $a.$ A massless string is attached to the ceiling of the cabin on which a bead of mass $m$ is sliding downwards with respect to string with an acceleration $a.$ The tension in the string is

A rocket is going upwards with accelerated motion. A man sitting in it feels his weight increased $5$ times his own weight. If the mass of the rocket including that of the man is $1.0\times {10}^4 \mathrm{kg}$. The force applied by rocket engine is $5\times {10}^4 \mathrm{N}$. $(\text{Take}\mathrm{ }g=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2})$

A motor cyclist at a speed of $5 \mathrm{m}/\mathrm{s}$ is describing a circle of radius $25 \mathrm{m}$. Find his inclination with vertical. What is the value of coefficient of friction between tyre and ground?

A car of mass $2000 \mathrm{kg}$ rounds a curve of radius $250 \mathrm{m}$ at $90 \mathrm{km}/\mathrm{hr}$. Compute its, centripetal force.

Show that the angle of banking is independent of mass of vehicle.

What is banking of roads? Why is it necessary?

Derive the expression for maximum safety speed with which vehicle should move along a curved horizontal road. State the significance of it.

Distinguish between centripetal and centrifugal force.

A ball connected with string is released at an angle$45°$ with the vertical as shown in the figure. Then the acceleration of the box at this instant will be (mass of the box is equal to mass of ball)

In the figure, the wedge is pushed with an acceleration of $10\sqrt{3} \mathrm{m} {\mathrm{s}}^{-2}$.  It is seen that the block starts climbing up on the smooth inclined face of wedge. What will be the time taken by the block to reach the top?

A car is moving on a plane inclined at $30°$ to the horizontal with an acceleration of $10 \mathrm{m} {\mathrm{s}}^{-2}$ parallel to the plane upward. A bob is suspended by a string from the roof. What is the angle in degrees made by the string with the vertical? (Make the assumption that the bob does not move relative to the car) $\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$ 

Suppose you are sitting on an accelerating trolley car.

Find the pseudo force acting on the block as viewed by the observer.

Suppose you are sitting on an accelerating trolley car.

Find the acceleration of the block as seen by the observer.