Q: A crate is $$1\ \mathrm{m}$$ wide and $$2\ \mathrm{m}$$ tall. A horizontal force of $$100\ \mathrm{N} is $$applied at a height of $$1.5\ \mathrm{m}$$ above the ground. What is the magnitude of the torque about the base of the crate?

$$\tau = 150\ \mathrm{N\cdot m}$$

Q: A uniform rod of length $$L$$ and mass $$M is $$attached to a hinge and supported by a string at an angle. What is the torque about the hinge due to gravity?

$$\tau = Mg\frac{L}{2}\sin\theta$$

Q: Which of the following is the correct condition for static equilibrium in two dimensions?

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

Question 1

A uniform rod of length $$L$$ and mass $$M is $$attached to a wall by a hinge at one end and held horizontally by a string at the other end. If the string is suddenly cut, what is the angular acceleration of the rod immediately after the cut? (Assume gravity acts downward and the moment of inertia of the rod about the hinge is $$I = \frac{1}{3}ML^2$.)

Accepted Answer

$$\alpha = \frac{3g}{2L}$$

Question 2

A solid disk of mass $$4.0\ \mathrm{kg}$$ and radius $$0.55\ \mathrm{m} is $$subjected to a $$30\ \mathrm{N}$$ force applied tangentially at its rim. What is the magnitude of the angular acceleration of the disk? (Moment of inertia for a solid disk: $$I = \frac{1}{2}MR^2$.)

Accepted Answer

$$\alpha = 24.8\ \mathrm{$$rad/s^2$$}$$

Question 3

Which of the following statements about static equilibrium for extended objects is correct?

Accepted Answer

Both the net force and the net torque on the object must be zero.

Question 4

A crate is $$1\ \mathrm{m}$$ wide and $$2\ \mathrm{m}$$ tall. A horizontal force of $$100\ \mathrm{N} is $$applied at a height of $$1.5\ \mathrm{m}$$ above the ground. What is the magnitude of the torque about the base of the crate?

Accepted Answer

$$	au = 150\ \mathrm{N\cdot m}$$

Question 5

A uniform rod of length $$L$$ and mass $$M is $$attached to a hinge and supported by a string at an angle. What is the torque about the hinge due to gravity?

Accepted Answer

$$	au = Mg\frac{L}{2}\sin	heta$$

Question 6

Three children are sitting on a merry-go-round. Child A is at the center, Child B is halfway to the rim, and Child C is at the rim. All have the same mass. Which child contributes the most to the total moment of inertia?

Accepted Answer

Child C at the rim

Question 7

A woman stands on one foot, on tiptoe. If her mass is $$60\ \mathrm{kg}$$, what is the magnitude of the normal force the floor exerts on her foot?

Accepted Answer

$$588\ \mathrm{N}$$

Question 8

Which of the following best describes the 'right-hand rule' for determining the direction of torque?

Accepted Answer

Point your fingers in the direction of $$\vec{r}$$, curl them toward $$\vec{F}$$; your thumb points in the direction of the torque.

Question 9

A car is parked on a hill. Under what condition will the car tip over rather than roll down the hill?

Accepted Answer

When the center of gravity passes outside the base of support

Question 10

A person tries to stand on tiptoe with their toes touching a wall. Why is it impossible to maintain balance in this position?

Accepted Answer

Because the person cannot shift their center of mass over their base of support

Question 11

Which of the following is the correct condition for static equilibrium in two dimensions?

Accepted Answer

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

Question 12

A force $$\vec{F} is $$applied at a distance $$r$$ from a pivot point, making an angle $$	heta$$ with the lever arm. What is the magnitude of the torque produced by this force?

Accepted Answer

$$	au = rF\sin	heta$$

Question 13

A massless rod is supported horizontally by a hinge at one end and a scale at the other. If a $$20\ \mathrm{N}$$ weight is hung $$0.75 of $$the way from the hinge, what is the reading on the scale if the rod is $$2\ \mathrm{m}$$ long?

Accepted Answer

$$20\ \mathrm{N}$$

Question 14

Which of the following will increase the stability of an object resting on a surface?

Accepted Answer

Lowering the center of mass and increasing the base of support

Question 15

A uniform rod of length $$L$$ and mass $$M is in $$static equilibrium, supported at both ends. If a mass $$m is $$hung at a distance $$d$$ from one end, what equation must be satisfied for equilibrium (taking torques about one end)?

Accepted Answer

$$Mg\frac{L}{2} + mgd = F$$_{other}$$L$$

Question 16

If a force is applied at an angle to a lever arm, which component of the force produces torque?

Accepted Answer

The component perpendicular to the lever arm

Question 17

A person is holding a heavy box with arms extended horizontally. Which of the following best explains why it is harder to hold the box with arms extended than with arms at your sides?

Accepted Answer

The torque due to the box's weight is greater when the arms are extended

Rotational Motion, Torque, and Static Equilibrium – Physics 201 Study Notes

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