Introduction to Radial & Tangential Acceleration

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 ${\text{cm/s}}^2)$

Q. When a particle moves in a uniform circular motion. It has

1. Radial velocity and tangential acceleration
2. Radial velocity and radial acceleration
3. Tangential velocity and radial acceleration
4. Tangential velocity and tangential acceleration

Q.

For a particle in uniform circular motion the acceleration $\overrightarrow{a}$ at a point $P(R,\theta )$on the circle of radius R is (here $\theta$ is measured from the x-axis)

1. $-\frac{v^2}{R}cos\theta \hat{i}+\frac{v^2}{R}sin\theta \hat{j}$

2. $-\frac{v^2}{R}sin\theta \hat{i}+\frac{v^2}{R}cos\theta \hat{j}$

3. $-\frac{v^2}{R}cos\theta \hat{i}+\frac{v^2}{R}sin\theta \hat{j}$

4. $\frac{v^2}{R}+\frac{v^2}{R}\hat{j}$

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. 

2. 

3. 

4. 

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. 

2. 
3. 
4. 

Q.

A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t₁ = 5.00 s, it is at point (5.00 m, 6.00 m) with velocity (3π m/s)$\hat{j}$ and acceleration in the positive x direction. At time t₂ = 10.0 s, it has velocity (-3π m/s)$\hat{i}$​ and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path if t₂ - t₁ is less than one period?

1. (15 m, 6 m)

2. (15 m, 0)

3. (-5 m, 0)

4. (-5 m, 6)

Q.

A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is (2.00 m/ $s^2$)$\hat{i}$ + (4.00 m/ $s^2$)$\hat{j}$ . At that instant and in unit-vector notation, what is the acceleration of the wallet? IIT JEE- 2001

1. 3 + 6

2. 3 + 3

3. 2 + 4

4. 4 + 2

Q.

A particle moves in a circle of radius 2.0 cm at a speed given by v = 4t, where v is in cm/s and t is in seconds.
Find the tangential acceleration at t =1 s.
Find total acceleration at t =1 s.

1. Tangential acceleration $=4cm/s^2$
   Radial acceleration $=16cm/s^2$

2. Tangential acceleration $=2cm/s^2$
   Total acceleration $=4\sqrt{5}cm/s^2$

3. Tangential acceleration $=4cm/s^2$
   Radial acceleration $=4\sqrt{5}cm/s^2$

4. Tangential acceleration $=2cm/s^2$
   Radial acceleration $=8cm/s^2$

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. For any type of motion, other than linear motion, there must be a acceleration.

1. radial
2. tangential
3. linear