Q: A wheel starts from rest and rotates with a constant angular acceleration of 2\text{ rad/s}^2. The total angle turned in the first 5\text{ seconds} is:

25\text{ rad}. \theta = \omega_0 t + \tfrac{1}{2}\alpha t^2 = 0 + \tfrac{1}{2}(2)(5)^2 = 25\text{ rad}.

Q: The angular velocity of a rotating body changes from 4\text{ rad/s} to 12\text{ rad/s} in 2\text{ seconds}. Its angular acceleration is:

4\text{ rad/s}^2. \alpha = \dfrac{\Delta\omega}{\Delta t} = \dfrac{12 - 4}{2} = 4\text{ rad/s}^2.

Q: A particle moves along a circle of radius 0.5\text{ m} with angular velocity 10\text{ rad/s}. Its linear (tangential) speed is:

5\text{ m/s}. v = \omega r = 10 \times 0.5 = 5\text{ m/s}.

Q: A body moves in a circle of radius 4\text{ m} with a constant speed of 8\text{ m/s}. Its centripetal acceleration is:

16\text{ m/s}^2. a_c = \dfrac{v^2}{r} = \dfrac{8^2}{4} = \dfrac{64}{4} = 16\text{ m/s}^2.

Q: A ceiling fan rotates at 300\text{ rpm}. Its angular velocity in rad/s is:

10\pi. \omega = \dfrac{2\pi N}{60} = \dfrac{2\pi \times 300}{60} = 10\pi \approx 31.4\text{ rad/s}.

Q: A wheel rotating at 20\text{ rad/s} is brought uniformly to rest in 10\text{ s}. The number of revolutions it makes before stopping is approximately:

16. Angular displacement \theta = \left(\dfrac{\omega_0 + \omega}{2}\right)t = \left(\dfrac{20 + 0}{2}\right)(10) = 100\text{ rad}. Number of revolutions = \dfrac{100}{2\pi} \approx 15.9 \approx 16.

Q: The angular displacement of a rotating body is given by \theta = 2t^3 radian. Its angular velocity at t = 2\text{ s} is:

24\text{ rad/s}. \omega = \dfrac{d\theta}{dt} = 6t^2. At t = 2\text{ s}, \omega = 6(4) = 24\text{ rad/s}.

Q: The angular velocity of a body varies as \omega = (4t^2 + 2t)\text{ rad/s}. Its angular acceleration at t = 1\text{ s} is:

10\text{ rad/s}^2. \alpha = \dfrac{d\omega}{dt} = 8t + 2. At t = 1\text{ s}, \alpha = 8 + 2 = 10\text{ rad/s}^2.

Q: The angular velocity of the Earth about its own axis is approximately:

7.27 \times 10^{-5}\text{ rad/s}. The Earth turns once in 24\text{ hours} = 86400\text{ s}, so \omega = \dfrac{2\pi}{86400} \approx 7.27 \times 10^{-5}\text{ rad/s}.

Question 1

A wheel starts from rest and rotates with a constant angular acceleration of 2	ext{ rad/s}^2. The total angle turned in the first 5	ext{ seconds} is:

Accepted Answer

25	ext{ rad}. 	heta = \omega_0 t + 	frac{1}{2}\alpha t^2 = 0 + 	frac{1}{2}(2)(5)^2 = 25	ext{ rad}.

Question 2

The angular velocity of a rotating body changes from 4	ext{ rad/s} to 12	ext{ rad/s} in 2	ext{ seconds}. Its angular acceleration is:

Accepted Answer

4	ext{ rad/s}^2. \alpha = \dfrac{\Delta\omega}{\Delta t} = \dfrac{12 - 4}{2} = 4	ext{ rad/s}^2.

Question 3

A particle moves along a circle of radius 0.5	ext{ m} with angular velocity 10	ext{ rad/s}. Its linear (tangential) speed is:

Accepted Answer

5	ext{ m/s}. v = \omega r = 10 	imes 0.5 = 5	ext{ m/s}.

Question 4

A body moves in a circle of radius 4	ext{ m} with a constant speed of 8	ext{ m/s}. Its centripetal acceleration is:

Accepted Answer

16	ext{ m/s}^2. a_c = \dfrac{v^2}{r} = \dfrac{8^2}{4} = \dfrac{64}{4} = 16	ext{ m/s}^2.

Question 5

A ceiling fan rotates at 300	ext{ rpm}. Its angular velocity in rad/s is:

Accepted Answer

10\pi. \omega = \dfrac{2\pi N}{60} = \dfrac{2\pi 	imes 300}{60} = 10\pi \approx 31.4	ext{ rad/s}.

Question 6

A wheel rotating at 20	ext{ rad/s} is brought uniformly to rest in 10	ext{ s}. The number of revolutions it makes before stopping is approximately:

Accepted Answer

16. Angular displacement 	heta = \left(\dfrac{\omega_0 + \omega}{2}ight)t = \left(\dfrac{20 + 0}{2}ight)(10) = 100	ext{ rad}. Number of revolutions = \dfrac{100}{2\pi} \approx 15.9 \approx 16.

Question 7

The angular displacement of a rotating body is given by 	heta = 2t^3 radian. Its angular velocity at t = 2	ext{ s} is:

Accepted Answer

24	ext{ rad/s}. \omega = \dfrac{d	heta}{dt} = 6t^2. At t = 2	ext{ s}, \omega = 6(4) = 24	ext{ rad/s}.

Question 8

The angular velocity of a body varies as \omega = (4t^2 + 2t)	ext{ rad/s}. Its angular acceleration at t = 1	ext{ s} is:

Accepted Answer

10	ext{ rad/s}^2. \alpha = \dfrac{d\omega}{dt} = 8t + 2. At t = 1	ext{ s}, \alpha = 8 + 2 = 10	ext{ rad/s}^2.

Question 9

The angular velocity of the Earth about its own axis is approximately:

Accepted Answer

7.27 	imes 10^{-5}	ext{ rad/s}. The Earth turns once in 24	ext{ hours} = 86400	ext{ s}, so \omega = \dfrac{2\pi}{86400} \approx 7.27 	imes 10^{-5}	ext{ rad/s}.

Question 10

If the angular velocity of a particle in circular motion is tripled while the radius is halved, its linear speed becomes:

Accepted Answer

1.5 times. v = \omega r, so v' = (3\omega)\left(\dfrac{r}{2}\right) = 1.5\,\omega r = 1.5\,v.

Question 11

The tangential acceleration a_t of a particle moving on a circle of radius r with angular acceleration \alpha is:

Accepted Answer

\alpha r. Differentiating v = \omega r with r constant gives a_t = \dfrac{dv}{dt} = r\dfrac{d\omega}{dt} = \alpha r. (\omega^2 r is the centripetal, not tangential, acceleration.)

Question 12

A particle on a circle of radius 2	ext{ m} speeds up uniformly from rest to 10	ext{ m/s} in 5	ext{ s}. Its tangential acceleration is:

Accepted Answer

2	ext{ m/s}^2. Tangential acceleration is the rate of change of speed: a_t = \dfrac{10 - 0}{5} = 2	ext{ m/s}^2.

Question 13

A particle moves on a circle of radius 2	ext{ m}. At the instant its speed is 10	ext{ m/s}, its centripetal acceleration is:

Accepted Answer

50	ext{ m/s}^2. a_c = \dfrac{v^2}{r} = \dfrac{100}{2} = 50	ext{ m/s}^2, directed towards the centre.

Question 14

A flywheel speeds up uniformly from 60	ext{ rpm} to 180	ext{ rpm} in 10	ext{ s}. Its angular acceleration is:

Accepted Answer

0.4\pi	ext{ rad/s}^2. \omega_0 = \dfrac{2\pi(60)}{60} = 2\pi and \omega = \dfrac{2\pi(180)}{60} = 6\pi	ext{ rad/s}. So \alpha = \dfrac{6\pi - 2\pi}{10} = 0.4\pi \approx 1.26	ext{ rad/s}^2.

Question 15

A wheel starting from rest rotates with constant angular acceleration 4	ext{ rad/s}^2. The angle turned during the 3^{	ext{rd}} second alone is:

Accepted Answer

10	ext{ rad}. Angle in the n^{	ext{th}} second: 	heta_n = \omega_0 + \dfrac{\alpha}{2}(2n - 1) = 0 + \dfrac{4}{2}(2 	imes 3 - 1) = 2 	imes 5 = 10	ext{ rad}.

Question 16

The angular velocity \omega of a body making n revolutions per second is:

Accepted Answer

2\pi n. One revolution corresponds to 2\pi radian, so n revolutions per second means \omega = 2\pi n	ext{ rad/s}.

Question 17

For a particle in uniform circular motion, which of the following remains constant?

Accepted Answer

The magnitude of its velocity. In uniform circular motion the speed is constant, but the direction of motion changes continuously. Hence velocity, acceleration and momentum are all changing vectors, while the magnitude of velocity (the speed) stays fixed.

Question 18

A wheel rotating at 10	ext{ rad/s} is subjected to a constant angular retardation of 2	ext{ rad/s}^2. The time it takes to come to rest is:

Accepted Answer

5	ext{ s}. \omega = \omega_0 - \alpha t \Rightarrow 0 = 10 - 2t \Rightarrow t = 5	ext{ s}.

Question 19

A flywheel starting from rest has a constant angular acceleration of 3	ext{ rad/s}^2. Its angular velocity after 6	ext{ s} is:

Accepted Answer

18	ext{ rad/s}. \omega = \omega_0 + \alpha t = 0 + 3 	imes 6 = 18	ext{ rad/s}.

Question 20

A wheel rotates at 120	ext{ rpm}. Its angular velocity is:

Accepted Answer

4\pi	ext{ rad/s}. \omega = \dfrac{2\pi N}{60} = \dfrac{2\pi 	imes 120}{60} = 4\pi \approx 12.57	ext{ rad/s}.

Angular Motion & Kinematics — MH-CET Physics MCQs with Solutions

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