Net Acceleration for Non Uniform Circular Motion

Q. Read each statement below carefully and state, with reasons, if it is true or false : (a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre (b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point (c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

Q. Why is change in magnitude of velocity in circular motion is 2vsinx/2? Here x= angle swept.

Q. A particle A moves along a corcle of radius R=50 cm so that its radius vector relative to an arbitrary point O on the circle rotates with cons†an t angular velocity ω=0.40 rad/s. Then modulus of the velocity v of the particle and the modulus of its total acceleration is:__________

Q. A thin wire of mass M and length L is bent to form a circular ring .The moment of inertia of this ring about its axis is

Q. 150. How to calculate average acceleration when body is moving in circular motion

Q. A thin circular loop of radius R rotates about its vertical diameter with an angular frequency w. Show that a small bead on the wire loop remains at its lowermost point for ω ≤ √ (g / R) . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √(2g / R )? Neglect friction.

Q. 12.For a body in circular motion with constant angular velocity the magnitude of the average acceleration over a period of half a Revolution is how many times the magnitude of its instantaneous acceleration

Q.

Starting from rest, a particle moves on a circle with constant angular acceleration $\alpha$. The time at which its tangential and normal acceleration become equal in magnitude is?

Q. A point on the rim of a disc starts circular motion from rest and after time $t$, it gains an angular acceleration given by $\alpha =3t-t^2$. The angular velocity after $2\text{sec}$ is:

1. $\frac{5}{3}\text{rad/s}$
2. $\frac{10}{3}\text{rad/s}$
3. $\frac{5}{2}\text{rad/s}$
4. $\frac{5}{4}\text{rad/s}$

Q. Find the moment of inertia of an annular disc of mass M and inner radius R1 and outer radius R2 about an axis tangential and perpendicular to plane 1. M/2(R1^2+3R2^2) 2. M/2(3R1^2+R2^2) 3. M/2(R1^2+5R2^2) 4. M/2(5R1^2+R2^2)

Q. 30.Is linear acceleration present in uniform circular motion

Q. A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn ?

Q.

A body is moving with a constant speed v in a circle of radius r. What is the angular acceleration?

1. 

2. 

3. 

4. 

Q. A racer drives his bike starting from rest on a circular track of radius $40\text{m}$ and having tangential acceleration of $3{\text{m/s}}^2$. What is the magnitude of net acceleration of the racer $5\text{s}$ after he starts to drive the bike?

1. $9{\text{m/s}}^2$
2. $6.37{\text{m/s}}^2$
3. $5.37{\text{m/s}}^2$
4. $7.55{\text{m/s}}^2$

Q. Angular position of a body undergoing circular motion varies with time as $\theta =2t^2+3$ radians. If radius of circular path is $1\text{m}$, the acceleration of body at $t=1\text{s}$will be

Q. A is the bottom most point of a particle describing a vertical circle of radius R. At point B, the acceleration of the particle is $g\sqrt{11}$. Find the velocity of the particle at top point C :

1. ${\left[gR\right(\sqrt{10}-2\left)\right]}^{\frac{1}{2}}$
2. ${\left[gR\right]}^{\frac{1}{2}}$
3. ${\left[gR\right(\sqrt{11}-2\left)\right]}^{\frac{1}{2}}$
4. None of these

Q.

If a particle is performing non-uniform circular motion with constant angular acceleration, then the linear acceleration of a particle as a function of time is _____. The particle starts from rest and moves along a circle of radius R.

Q. A particle moves in a circle of radius $25cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is

1. ${\pi }^2$
2. $8{\pi }^2$
3. $4{\pi }^2$
4. $2{\pi }^2$

Q. A particle is revolving in a circular path of radius25 m with constant angular speed 12 rev/min. Thenthe angular acceleration of particle is

Q.

A mass of 100 gm is tied to one end of a string 2 m long. The body is revolving in a horizontal circle making a maximum of 200 revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is (approximately)

1. 8.76 N

2. 8.94 N

3. 89.42 N

4. 87.64 N

Q. Find the angle between the net acceleration vector and tangential acceleration vector for a particle moving in a circle of radius $4m$ with its speed increasing at $3m/s$ every second, when the speed of the particle is $4m/s$.

1. ${37}^{\circ }$
2. ${53}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q. The angular position of a particle revolving about an axis is given by 0(t) = t^2- 3t+ 4 radian. Find the acceleration of the point at time t = 2 s. Given radius of circular path is 1 m. (1) 2 m/s2 (2) 1 m/s2 (4) 5 m/s? (3) 5 m/s2

Q. For a particle moving along circular path, the radial acceleration $a_r$ is proportional to time $t$. If $a_t$ is the tangential acceleration, then which of the following will be independent of time?

1. $a_t$
2. $a_r.a_t$
3. $\frac{a_r}{a_t}$
4. $a_r(a_t{)}^2$

Q. Find the moment of inertia of an annular disc of mass M and inner radius R1 and outer radius R2 about an axis tangential and perpendicular to plane 1. M/2(R1^2+3R2^2) 2. M/2(3R1^2+R2^2) 3. M/2(R1^2+5R2^2) 4. M/2(5R1^2+R2^2)

Q. A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively are $\overrightarrow{\omega },\overrightarrow{v},\overrightarrow{\alpha }$ and $\overrightarrow{a_c}$. Which of the following relations is not correct?

1. $\overrightarrow{\omega }\perp \overrightarrow{v}$
2. $\overrightarrow{\omega }\perp \overrightarrow{\alpha }$
3. $\overrightarrow{\omega }\perp \overrightarrow{a_c}$
4. $\overrightarrow{v}\perp \overrightarrow{a_c}$

Q. A stone tied to the end of a string $1\text{m}$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolutions in $44$ seconds, what is the magnitude and direction of acceleration of the stone?

1. ${\pi }^2{\text{ms}}^{-2}$ and direction along the radius towards the centre.
2. ${\pi }^2{\text{ms}}^{-2}$ and direction along the radius away from the centre.
3. ${\pi }^2{\text{ms}}^{-2}$ and direction along the tangent to the circle.
4. $\frac{{\pi }^2}{4}{\text{ms}}^{-2}$ and direction along the radius towards the centre.

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

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

Q.

The maximum velocity (in $m{s}^{–1}$) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

1. 60

2. 30

3. 15

4. 25

Q. 17.Lorry and car with same kE came in rest with equal force , which will cover less distance

Q.

A road is 10 m wide. Its radius of curvature is 50 m. The outer edge is above the lower edge by a distance of 1.5 m. This road is most suited for the velocity

1. 2.5 m/sec

2. 4.5 m/sec

3. 6.5 m/sec

4. 8.5 m/sec