Question

4 pts Question 16 Examine the gyroscope diagram here. What are the correct directions (designated as the blue arrows a-d) of the following in this order: 1) torque, 2) angular momentum, and 3) precession? mg cd, c b,a,c Ccb, a cab a, b, c

Answer 1

I si (change in I due to Kit torque caused by l aitot weight of wheel Direction of wa precession o (new angular momentum) (position of wheel) E = mg (weight)

The above figure shows the free body diagram of the wheel.

From the diagram, the weight of the wheel,

$\overrightarrow{F}=-mg\ \widehat{z}$

The position of the wheel with respect to the origin,

$\overrightarrow{r}=b\ \widehat{x}$

The rotation of the wheel from its axis,

スニーは

(a) The torque on the wheel due to its weight is,

$\overrightarrow{\tau}=\overrightarrow{r}\times \overrightarrow{F}\\ \overrightarrow{\tau}=(b\widehat{x})\times (-mg\widehat{z})\\ \overrightarrow{\tau}=mgb\ \widehat{y}$

The direction of the torque towards the positive y-axis means towards c.

(b) The angular momentum of the wheel due to its rotation is,

$\overrightarrow{L}=I\overrightarrow{\omega}\\ \overrightarrow{L}=-I\omega\ \widehat{x}$

The direction of the angular momentum towards the negative x-axis means towards a.

(c) From the free body diagram, we can see that there is a change in the angular momentum $(\overrightarrow{\Delta L})$ due to the torque acting on the wheel which causes new angular momentum$(\overrightarrow{L'}=\overrightarrow{L}+\overrightarrow{\Delta L})$.

Due to this change in angular momentum, the wheel precesses in a clockwise direction around positive z-axis means towards b.