Question

During a certain period of time, the angular position of swinging door is described by O=5.00+10.0t+2.00t^2
Where O is in rad and t is in second.
Determine the angular position, the angular speed and the angular acceleration of the door
a) at t=0
b)at t=3.00s

Answer 1

Answer on Question #84756- Physics - Mechanics/Relativity

Question: During a certain period of time, the angular position of swinging door is described by $O = 5.00 + 10.0t + 2.00t^2$

Where $O$ is in rad and $t$ is in second.

Determine the angular position, the angular speed and the angular acceleration of the door

a) at $t = 0$

b) at $t = 3.00s$

Answer:

By definition, angular velocity $\omega$ and angular acceleration $\alpha$ are defined as:

$$\omega = \frac{d\theta}{dt}, \quad \alpha = \frac{d\omega}{dt}.$$

Calculating the derivatives explicitly, one can obtain:

$$\omega = 10 + 4t, \quad \alpha = 4.$$

Substituting numerical values, we get:

$$\theta(0) = 5 \text{rad}, \quad \theta(3s) = 53 \text{rad}$$ $$\omega(0) = 10 \text{rad} / s, \quad \omega(3s) = 22 \text{rad} / s.$$ $$\alpha(0) = \alpha(3s) = 4 \text{rad} / s^2$$

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