Question 199: Work, Energy and Power & Circular Motion

Question

A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $	heta_1$ in first 2 s and a further angle $	heta_2$ in the next 2 s , the ratio $	heta_1: 	heta_2$ is

Accepted Answer

Let the
initial angular velocity
be $\omega_0 = 0$ (since the wheel is initially at rest).
Let the
angular acceleration
be $\alpha$.
Angular displacement in time $t$ is:
$ 	heta = \omega_0 t + \frac{1}{2} \alpha t^2 $
First 2 seconds ($t = 2$ s)
$ 	heta_1 = 0 \cdot 2 + \frac{1}{2}\alpha (2)^2 = \frac{1}{2}\alpha \cdot 4 = 2\alpha $
Next 2 seconds ($t = 4$ s total, $t = 2$ s extra)
Total angle covered in 4 seconds:
$ 	heta_{	ext{total}} = 0 \cdot 4 + \frac{1}{2}\alpha (4)^2 = \frac{1}{2}\alpha \cdot 16 = 8\alpha $
So,
angle covered in the next 2 seconds
($	heta_2$):
$ 	heta_2 = 	heta_{	ext{total}} - 	heta_1 = 8\alpha - 2\alpha = 6\alpha $
Ratio $	heta_1 : 	heta_2$
$ 	heta_1 : 	heta_2 = 2\alpha : 6\alpha = 1 : 3 $
Correct option: D

Answer

$1: 6$

Answer

$6: 1$

Answer

$3: 1$

Answer

$1: 3$

Work, Energy and Power & Circular Motion

A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle \theta_1 in first 2 s and a further angle \theta_2 in the next 2 s , the ratio \theta_1: \theta_2 is

Choose the correct answer: