PHYS 1401 – General Physics I

Rolling without Slipping

Leader: _________________________ Recorder: __________________________

Skeptic: _________________________ Encourager: ________________________

Materials

Toy Tractor

String

Stop Watch

Meter Stick

Masking Tape

Introduction

In this brief activity we will examine the relationship between linear and rotational variables by investigating the conditions for rolling without slipping. Our apparatus consists of an electric chassis that travels at a constant velocity. We will examine the relationship between linear motion of the chassis and the rotational motion of the wheels that drive the chassis.

Procedure

1. Set up and Preliminary measurements

Measure and record the circumference of the tread on the toy chassis.

Tread Length = _____________________________

Measure and record the radius and determine the circumference of the drive wheel on the toy chassis. You may need to turn on the chassis without the tread to identify the drive wheels.

Drive Wheel Radius = ___________________

Drive Wheel circumference = ____________________

Place a very small piece of masking tape on the edge of the tread as a reference mark and a similar piece on the drive wheel.

2. Data Collection

P2) Predict how far the tractor will travel when the tread makes three complete revolutions. Explain your reasoning.

Place a piece of masking tape on the table to act as a starting line.

Run the tractor from the starting line until the treads make three complete revolutions. Mark the point that the tractor treads completed three revolutions with a second piece of tape. Note that you may want to use to use light pressure with a meter stick to guide the tractor along the track.

Q3) Measure and record the distance traveled by the tractor.

Distance = __________________________

Q4) How close was your measured value to your predicted value?

P5) Predict how many revolutions the drive wheel will make when the tractor travels between the two lines. Explain your reasoning.

Run the tractor between the two lines again, but this time count the number of revolutions made by the drive wheel.

Q6) Record the number of revolutions made by the drive wheels

# Revolutions = _____________________

Q7) How close was your prediction to the measured value?

The condition that an object rolls without slipping is that the distance traveled in a line equals the arc length turned out by the wheel.

Q8) Based on your measurements, does it seem reasonable to describe the motion of the tractor as rolling without slipping? Explain.

Q9) If the wheel did slip, how would the distance traveled in a line by the tractor compare to the arc length turned out by the wheel? (i.e. >, =, <) Explain.

The condition for rolling without slipping can be expressed as s = NC where s is the distance traveled, N is the number of revolutions of the drive wheel, and C is the circumference of the drive wheel, C = 2πr. Substituting we can write s = N(2πr). (1)

Q10) Find an expression for the angle, θ, in radians turned by the wheel as it turns through N rotations.

Q11) Use your expression to substitute for N in equation (1) above.

The expression you’ve just found is a standard way of expressing the condition for rolling without slipping.

Run the tractor between the lines again while timing it.

Q12) Determine the Average Speed of the tractor. Show your work.

Q13) Determine the average angular velocity of the drive wheel. Show your work. Express your answer in units of rad/s.

Q14) Determine the ratio of the average speed of the tractor over the angular velocity of the drive wheel.

Q15) What are the units of the ratio.

Q16) Divide both sides of your answer to Q11) by t to find an expression relating the average speed and the average angular velocity of the wheel.

Q17) What does your answer to Q16) predict should be the ratio of the average speed over the angular velocity?

Q18) How does the value predicted by Q16) compare to the measured value?

Q16 gives a second expression for the condition that an object rolls without slipping.