Introduction to Radial & Tangential Acceleration

Q.

At t₁ = 2.00 s, the acceleration of a particle in counter clockwise circular motion is It moves at constant speed. At time t₂ = 5.00 s, the particle's acceleration is What is the radius of the path taken by the particle if t₂ - t₁ is less than one period?

1. $\frac{40}{{\pi }^2}$

2. $\frac{360}{{\pi }^2}$
3. $\frac{30}{{\pi }^2}$
4. $\frac{60}{{\pi }^2}$

Q. A body moving in a circular path with a constant speed has a constant .

1. velocity
2. momentum
3. kinetic energy
4. acceleration

Q. The angular velocity of a particle moving in a circle of radius $50cm$ is increased in $5$ min from $100$ revolutions per minute to $400$ revolutions per minute. Find the tangential acceleration of the particle.

1. $60m/s^2$
2. $\frac{\pi }{30}m/s^2$
3. $\frac{\pi }{15}m/s^2$
4. $\frac{\pi }{60}m/s^2$

Q. A particle is initially at rest, moves along in a circle of radius $R=2\text{m}$ with an angular acceleration $\alpha =\frac{\pi }{8}{\text{rad/sec}}^2$. The magnitude of average velocity of the particle over the time it moves by half of the circle is

1. $4\text{m/s}$
2. $3\text{m/s}$
3. $2\text{m/s}$
4. $1\text{m/s}$

Q. A particle is moving on a circular track of radius 4 m such that its tangential acceleration is 2t m/$s^2$. If the particle starts from rest, then at what time the angle between velocity and acceleration will be ${45}^{\circ }$?

1. 5 sec
2. 4 sec
3. 3 sec
4. 2 sec

Q. A small block is placed on a turn table. The coefficient of static friction between the block and the table is ${\mu }_s=0.5$. If the turn table is rotating with constant angular acceleration $\alpha =3{\text{rad/s}}^2$, what will be the angular speed at which the block begins to slip on the table ?
Given $r=1\text{m},g=10{\text{m/s}}^2.$

1. $1\text{rad/s}$
2. $2\text{rad/s}$
3. $3\text{rad/s}$
4. $4\text{rad/s}$

Q. The angular velocity of a particle moving on a circular path of radius $50\text{cm}$ is increased in $5\text{min}$ from $100\text{rpm}$ to $400\text{rpm}$. Find the magnitude of tangential acceleration of the particle.

1. $60{\text{ms}}^{-2}$
2. $\frac{\pi }{30}{\text{ms}}^{-2}$
3. $\frac{\pi }{15}{\text{ms}}^{-2}$
4. $\frac{\pi }{60}{\text{ms}}^{-2}$

Q. Two bodies $A$ & $B$ rotate about an axis such that angle ${\theta }_A$ (in radians) covered by first body is proportional to square of time, & ${\theta }_B$ (in radians) covered by second body varies linearly. At $t=0,{\theta }_A={\theta }_B=0$. If $A$ completes its first revolution in $\sqrt{\pi }\text{s}$ & $B$ needs $4\pi \text{s}$ to complete half revolution, then angular velocities ${\omega }_A$ & ${\omega }_B$ at $t=5\text{s}$ are in the ratio

1. $4:1$
2. $20:1$
3. $80:1$
4. $20:4$

Q. In the non-uniform circular motion shown below, the magnitude of change in tangential acceleration of the particle is

1. $4m/s^2$
2. $16m/s^2$
3. $0m/s^2$
4. $2m/s^2$

Q. The bob of a pendulum at rest is given an impulse to impart a horizontal velocity $\sqrt{gl}\text{m/s}$ where $l$ is the length of the pendulum. Find the tangential acceleration at the point where velocity of the bob is zero.

1. $8.66{\text{m/s}}^2$
2. $5{\text{m/s}}^2$
3. $7.07{\text{m/s}}^2$
4. $10{\text{m/s}}^2$

Q. A particle rests on the top of a smooth hemisphere of radius $r$. It is imparted a horizontal velocity of $\sqrt{gr}$. Find the normal reaction when it makes an angle $\theta ={60}^{\circ }$ with vertical.

1. $1.5mg$
2. $2.5mg$
3. $-1.5mg$
4. $0$

Q. Tangential acceleration of a particle moving in a circle of radius $1\text{m}$ varies with time t as shown in figure (initial velocity of particle is zero). Time after which total acceleration of the particle makes an angle of ${30}^{\circ }$ with radial acceleration is:

1. $4\text{sec}$
2. $\frac{4}{3}\text{sec}$
3. $2^{2/3}\text{sec}$
4. $\sqrt{2}\text{sec}$

Q.

A particle moves in a circle of radius 20 cm. Its linear speed is given by v = 2t, where t is second and v in metre/second. Find the radial and tangential acceleration at t = 3 s.

1. $a_r=1.8m/s^2$

2. $a_r=180m/s^2$

3. $a_t=6m/s^2$

4. $a_t=2m/s^2$

Q. A particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\overrightarrow{a}=(4\hat{i}+3\hat{j})m/s^2$ and $\overrightarrow{p}=(8\hat{i}-6\hat{j})kgm/s$. The motion of the particle is

1. Uniform circular motion
2. Accelerated circular motion
3. Decelerated circular motion
4. We cannot say anything with $\overrightarrow{a}$ and $\overrightarrow{p}$ only.

Q. A particle moves in a circle of radius $3.5\text{cm}$ at a speed given by $v=8t$, where $v$ is in $\text{cm/s}$ and $t$ in seconds. Find the tangential acceleration at $t=2\text{s}$. (in ${\text{cm/s}}^2)$

1. $32{\text{cm/s}}^2$
2. $24{\text{cm/s}}^2$
3. $16{\text{cm/s}}^2$
4. $8{\text{cm/s}}^2$

Q. The acceleration affects the speed of a body and acceleration affects the direction.

1. tangential
2. vibratory
3. radial
4. rectilinear

Q. A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its net acceleration vector $\overrightarrow{a}$ is correctly shown in which of the following options ?

1. 
2. 
3. 
4. 

Q. Wheel A of radius $r_A=10\text{cm}$ is coupled by belt B to a wheel C of radius $r_c=25\text{cm}$. The angular speed of the wheel A is increased from rest at a constant rate of $1.6{\text{rad/s}}^2.$ Find the time needed for wheel C to reach an angular speed of $100\text{rev/min},$ assuming that the belt does not slip.

1. 4 seconds
2. 9 seconds
3. 16 seconds
4. 25 seconds

Q. A point moves along a circle of radius $4\text{m}$. The distance $x$ is related to time by $x=c{t}^3$. What should be the value of $c$, so that the tangential acceleration is equal to the normal acceleration when its linear velocity is $4\text{m/s}$?

1. $0.288{\text{m/s}}^2$
2. $0.288{\text{m/s}}^3$
3. $0.333{\text{m/s}}^2$
4. $0.333{\text{m/s}}^3$

Q. A particle is moving on a circular track of radius 4 m such that its tangential acceleration is 2t m/$s^2$. If the particle starts from rest, then at what time the angle between velocity and acceleration will be ${45}^{\circ }$?

1. 5 sec
2. 4 sec
3. 3 sec
4. 2 sec

Q. The body is moving in a circular path, the component of velocity in the radial direction is

1. $0$
2. speed of the body
3. $\frac{v}{R}$
4. none of the above

Q. A particle is initially at rest, moves along in a circle of radius $R=2\text{m}$ with an angular acceleration $\alpha =\frac{\pi }{8}{\text{rad/sec}}^2$. The magnitude of average velocity of the particle over the time it moves by half of the circle is

1. $4\text{m/s}$
2. $3\text{m/s}$
3. $2\text{m/s}$
4. $1\text{m/s}$

Q. The length of the seconds hand in a wall clock is $10\text{cm}$. The magnitude of velocity and acceleration of its tip are

1. ${10}^{-2}\text{m/s}$ and ${10}^{-3}{\text{m/s}}^2$
2. ${10}^{-2}\text{m/s}$ and ${10}^{-4}{\text{m/s}}^2$
3. ${10}^{-1}\text{m/s}$ and ${10}^{-2}{\text{m/s}}^2$
4. ${10}^{-2}\text{m/s}$ and ${10}^{-2}{\text{m/s}}^2$

Q. A $10\text{kg}$ ball attached at the end of a rigid massless rod of length $(L=1\text{m})$ rotates at constant speed in a horizontal circle of radius $0.5\text{m}$ with a period of $1.57\text{s}$, as shown in the figure. The force exerted by the rod on the ball is (Take $g=10{\text{ms}}^{-2}$ & $\pi =3.14$)

1. $20\sqrt{41}\text{N}$
2. $10\sqrt{41}\text{N}$
3. $20\sqrt{20}\text{N}$
4. $10\sqrt{20}\text{N}$