Question 1

A ball attached to a rope is swung in a circle, experiencing a force perpendicular to its velocity. According to $$\vec{F} = \frac{d\vec{P}}{dt}$$, what happens to the ball's motion?

Accepted Answer

The ball will turn left with no change in speed.

Question 2

Which equation represents the first condition for static equilibrium?

Accepted Answer

$$\sum \vec{F} = 0$$

Question 3

A gyroscope is spinning with angular momentum $$\vec{L}$$ and experiences a torque $$\vec{	au}$$ perpendicular to $$\vec{L}. $$What happens to the axis of rotation?

Accepted Answer

The axis of rotation changes direction while angular speed remains constant.

Question 4

A nonrotating flywheel falls as shown in the diagram. What causes its free end to follow a circular path?

Accepted Answer

The weight creates a torque around the pivot.

Question 5

When a rotating flywheel is supported at a pivot, what is the effect of the torque due to its weight?

Accepted Answer

It causes the angular momentum to precess around the pivot.

Question 6

Which of the following is NOT a condition for static equilibrium?

Accepted Answer

Zero net acceleration.

Question 7

A car is parked on a slope. Under what condition will the car tip over?

Accepted Answer

When the center of gravity is outside the area of support.

Question 8

A uniform meter stick with a rock of equal mass attached to its left end is balanced on a pivot. Where should the pivot be placed?

Accepted Answer

0.25 m from the left end.

Question 9

Which equation represents the second condition for static equilibrium?

Accepted Answer

$$\sum \vec{	au} = 0$$

Question 10

A ladder rests against a frictionless wall and is in equilibrium. Which force does the wall exert?

Accepted Answer

A normal force perpendicular to the wall.

Question 11

If the center of gravity of an object is not above or below the point of suspension, what happens?

Accepted Answer

There will be a net torque and the object will not be in equilibrium.

Question 12

A mug is suspended from two different points. How can you experimentally locate its center of gravity?

Accepted Answer

The intersection of vertical lines from each suspension point passes through the center of gravity.

Question 13

Which scenario violates the first condition for equilibrium but satisfies the second?

Accepted Answer

An object with a net upward force but zero net torque.

Question 14

A vehicle tips over when its center of gravity is outside the area of support. What practical design change can reduce tipping risk?

Accepted Answer

Lowering the center of gravity.

Question 15

In the ladder problem, why is it advantageous to compute torques about the base of the ladder?

Accepted Answer

It eliminates unknown forces at the base from the torque equation.

Question 16

A spinning gyroscope precesses around its pivot. What is the direction of precession when viewed from above if the angular momentum points to the right?

Accepted Answer

Counterclockwise.

Question 17

Which of the following best describes the center of gravity for an object in a uniform gravitational field?

Accepted Answer

It coincides with the center of mass.

Question 18

If an object is supported at several points, where must its center of gravity be for equilibrium?

Accepted Answer

Within the area bounded by the supports.

Question 19

A ladder of mass $$m$$ and length $$L$$ leans against a frictionless wall at angle $$	heta. A $$person of mass $$M$$ stands a distance $$d up $$the ladder. Which equation must be satisfied for equilibrium?

Accepted Answer

$$\sum F_x = 0$$, $$\sum F_y = 0$$, $$\sum 	au = 0$$

Question 20

A rock of mass $$m is $$attached to the left end of a uniform meter stick of mass $$m. If $$the stick is balanced on a pivot, what is the total torque about the pivot?

Accepted Answer

Zero, if the pivot is placed at 0.25 m from the left end.

Precession and Static Equilibrium: Concepts, Conditions, and Applications

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