Rotational Motion

Investigation 5

Rotational Motion

1. The picture shows an LP record (you all remember LP’s?) as viewed from above. The record is turning in a clockwise direction at 33 1/3 rpm. Two bugs are located at positions A and B on the record.

a. Are the bugs accelerating? Explain.

Yes. Their directions of motion are changing.

b. Which bug is moving at the higher speed?

B

c. Which bug has the higher angular (rotational) speed?

Same angular speed.

d. When bug B is at the position shown in the picture, in what direction is bug B traveling (1, 2, 3, 4, or 5)?

2

e. When bug B is at the position shown in the picture, suppose bug B falls off the edge of the rotating LP. While falling off the record, other than gravity, what other forces are acting on the bug?

None.

f. On what path (1, 2, 3, 4, or 5) will the bug most likely travel after falling off?

2

2. A long, uniform rod is rotated about axes through A, B, and C. The rod is rotated around each axis. Rank the axes from the largest moment of inertia produced to the smallest moment of inertia produced.

A, C, B

When trying to evaluate the relative moments of inertia, what did you look for when finding the largest moment of inertia?

Location of the mass of the rod – the further from the axis, the greater the moment of inertia.

3. A wrench is being used to loosen the nut on a bolt. A 100 N force is applied at different positions on the wrench and in different directions.

a. Which force (or forces) produces the greatest torque?

E

b. Which force (or forces) produces the least torque?

F

4. Draw an X to show where the center of mass of the following objects is located.

a. a uniform thin rod / b. a uniform rectangular plate / c. a donut

If each of the above objects is slightly tipped to the side, does their center of mass move up, move down, or stay at one level?

a. down b. up c. stays at one level

Indicate whether each of the objects is in stable equilibrium, unstable equilibrium, or neutral equilibrium.

a. unstable b. stable c. neutral

5. The picture shows a car is traveling at a constant speed of 50 km/hr along a circular road that is curving to the left.

a. Annie, , who is sitting in the passenger seat with a seatbelt, feels a horizontal force acting on her in addition to the gravitational force and the upward force the seat exerts on her. Name the horizontal force (i.e., what horizontal force is pushing or pulling on Annie – the force of what on what?), and draw the direction of the force on the picture.

Force of the seatbelt on Annie.

(This force is the centripetal force.)

b. Name the centrifugal force.

Force of Annie on the seatbelt.

c. Is there also a force acting on the car that causes it to travel in the curved path? If so, then what is the force and in what direction does it point?

Friction force of the road on the tires of the car pointing inward toward the center of the curve.

3. A 600 N physics student is sitting on a bathroom scale that is resting on the seat of a chair on a Ferris wheel. (Santa Monica pier has a very nice one.)

a. What is reading on the scale when the Ferris wheel is not moving?

600 N

Suppose the Ferris wheel is now moving at a constant rotational speed. In this case, we know that the net force acting on the student is the centripetal force, with its direction being toward the center of the circle.

b. Draw vectors to represent the forces acting on the student when she is at the top and at the bottom of the circular path, and show the direction of the net force.

top: bottom:

What is the reading on the scale when she is at the top of the circular path and then at the bottom of the circular path? (600 N, greater than 600 N, or less than 600 N) The diagram above showing the vectors will help.

top: less than 600 N bottom: greater than 600 N

c. The readings on the scale when the student is at positions A and B will both be 600 N. Do you know why? (rhetorical question)

5. a. When an ice skater, who is spinning, moves her arms and legs in closer to the axis of rotation of her body, what happens to her moment of inertia?

moment of inertia decreases

b. What happens to her angular velocity (rate of spin)?

angular speed increases

c. Why did the above occur?

Conservation of angular momentum: (moment of inertia) x (angular speed) = constant value

6. If all the ice at the poles of the earth were to melt, then the water trapped in the ice would distribute itself evenly over the earth. Would the length of the day get longer or shorter? Why?

The length of the day would increase. The water in the form of ice at the poles would distribute itself over the surface of the earth resulting in some of the water moving further away from the axis of rotation. The moment of inertia increases and the angular speed decreases.