Name: Partner: Date: 8 Centripetal Force Introduction An object is in uniform circular motion if it travels around a circle at a constant speed. For objects traveling in a circle, it is useful to measure speed as angular velocity, which is the measure of angular displacement per unit time. We can relate angular velocity to linear velocity with the relationship v = rw where r is the radius of the circle and w is the measured angular velocity. Although the speed of the object does not vary, the velocity vector is changing direction and the object is therefore accelerating. (Acceleration is defined as a change in velocity, which can be a change in magnitude, direction, or both.) This acceleration is called centripetal acceleration and is defined as ac where v is the linear velocity of the object. The centripetal acceleration is always directed radially inwards (towards the center of the circle). Because the object is accelerating, it must be experiencing a net force of magnitude mac that is causing it to move in a circle. Pre-lab and Discussion Questions Pre-Lab Questions This part of the lab is to be completed prior to class. You MUST show it to your instructor upon arrival or else no credit will be given for this section. 1. A car is driving in a circle at a constant speed of 20 mph. Is the car accelerating? Explain your answer. [5 pts] 2. Determine the direction of the acceleration for the velocity vectors shown in the figure below. Hint - remember a = (vf - vi)/t. [3 pts] V2 V1 653. If there is acceleration, there should be a force according to Newton's Second Law: Fnet = ma The centripetal acceleration is given by ac = . What is the formula for the centripetal force if you know an object's speed and what is its direction? [2 pts] Discussion Questions This part of the lab is to be completed with your group in class. Centripetal force is a net force, therefore the important question when studying uniform circular motion is what is providing the centripetal force. 4. Consider the motion of the Moon around the Earth. If M is the mass of the Earth, m the mass of the Moon, and R the radius of the Moon's orbit, answer the following questions: (a) What provides the centripetal force? [3 pts] (b) What force is stronger, the Earth pulling on the Moon or the Moon pulling on the Earth? Explain your answer. [3 pts] (c) Given Newton's Law for the gravitational force: F = GMm R2 and Newton's Second Law Fnet = ma, find an expression for the Moon's orbital speed. Hint - You will also need to use the definition of centripetal acceleration. [4 pts] 66Application Question 6. The figure below shows the pendulum at some angle 0: (a) Using the provided figure, draw the free-body diagram for the pendulum. What is providing the centripetal force for the pendulum? [5 pts] (b) Using conservation of energy, find an expression for the speed of the pendulum at any angle 0. [5 pts] (c) Calculate the speed of your pendulum given an initial angle of 0 = 60. Does this make sense compared to what you measured? [5 pts] Hint - be aware of units! 69