AP Physics B I.E

Circular Motion and Rotation

I.E.1 Uniform Circular Motion

Behold the ball moving in a circular path: Who will it hit?

Ex. Find the speed of the earth at the equator as it rotates about its axis if the radius of the earth is 6.37 EE 6 m.

Centripetal acceleration is a vector, directed toward the center

of the circle.

Centripetal force always points towards the center of the circle

and continually changes directions as the object moves. It

is not a new force. It is merely the way we describe the net force pointing towards the center of the

circle.

What is the centripetal force for . . .

• The clothes in a washing machine that is in the “spin” cycle?

• A car making a circular turn?

• A roller coaster making a circular turn?

• The “Gravitron”?

• The Earth as it orbits the Sun?

Ex. An object of mass 5.0 kg moves at a constant speed of 6.0 m/s in a circular path of radius 2.0 m. Find the object’s acceleration and the force that keeps it moving in a circular path.

Ex. A 10.0 kg mass is attached to a string that has a breaking strength of 200 N. If the mass is whirled in a horizontal circle of radius 80 cm, what maximum speed can it have?

Ex. Car on a Curve: A car travels with a velocity of 13.4 m/son a level circular track with a radius of 50.0 m. What is thecoefficient of static friction between the car and the road inorder to make the circular turn without sliding?

Ex. A roller coaster car has a speed of 15 m/s at the top of a circular loop (where the car is upside down). If the diameter of the loop is 40.0 m and the total mass of the car and passengers is 1200 kg, find the magnitude of the normal force exerted by the track on the car.

Ex. What is the normal force for the roller coaster when the car is at the bottom of the circle?

Concept Question: A roller coaster makes a vertical loop. What is the direction of the acceleration of the coaster at the a) top of the loop? b) bottom of the loop?

Concept question: Is it harder for a trapeze artist to hold his partner

when hanging vertically at rest, or swinging through the bottom of the

arc?

Ex. A 0.150 kg ball on the end of a 1.10 m long string is swungin a vertical circle. a) Find the minimum speed the ball must have at the top of the circle to maintain its circular path. b) Calculate the tension of the string at the bottom of the circular path if the ball is moving at twice the speed in part a.

Concept Question: A ball attached to a string is whirled in a horizontal circle with radius r. If the radius of the string is changed to ½ r and the same centripetal force is applied to the string, what is the new speed of the ball?

Ex. A car with mass m and speed v, and a second car with mass 1/2m and speed v, both travel the same horizontal circular path. If the frictional force required to keep the larger car on the road is F, what is the frictional force required to keep the smaller car on the road without skidding?

I.E.2 Torque and Rotational Statics

Which force will rotate the rod, fixed at the left end?

F3

F1F2

F4

pivot

Torque is that which creates rotation. What are three factors

that affect torque?

Now, using the formula, explain why only F4 produces torque.

Ex. A student pulls down with a force of 40 N on a rope that winds around a pulley of radius 5.0 cm. What is the torque produced?

If a body is in equilibrium, neither its linear (translational) motion,

nor its rotational motion changes. So, ΣF = 0 and Στ = 0.

By convention, ccw torques are positive and cw torques are

negative.

Ex. What is the net torque on the cylinder below which rotates about its center?

F1 = 100 N

F2 = 80 N

12 cm8 cm

Ex. An object weighing 60 N is set on a rigid beam of uniform mass, and a weight of 10 N, rests on a pivot, as shown below. What is the magnitude of the vertical force that must be applied at the right end of the beam to keep it from rotating?

60 N

4 m 6 m

F