Download Acceleration Characteristics for Circular Motion

Centripetal Force Requirement
Newton's first law of motion states that…An object in motion tends to stay in motion with the
same speed and in the same direction unless acted upon by an unbalanced force.
In what path do objects naturally travel? Straight lines.
What is required for objects to move in circles? An unbalanced force.
Newton's second law of motion says that… if acceleration is present then net force is present in
the same direction.
Does an object moving in a circle experience acceleration if it is moving around the perimeter of the
circle with a constant speed? yes
If so, then what does Newton’s Second Law imply about the net force? Net force is always present
during circular motion, and points towards the center.
What is a centripetal force? Any force pushing or pulling the object toward the center of the
circular path. The word centripetal describes DIRECTION only.
Is centripetal force a new type of force? NO! A centripetal force is either N, T, Ff, or w.
Give three examples of centripetal force.
1. Weight of the earth towards the sun causes our orbit.
2. Banked turns provide normal force towards the center.
3. Motorcycles leaning in to the turns provide normal force.
What are centrifugal forces? No such thing! (See www.physicsclassroom.com for more.)
What are the relevant equations for centripetal force? Fc = mac
What is the relationship between centripetal force and velocity? Since ac = v2/R, and Fc = mac,
Fc = m v2/R. Therefore, Fc  v2
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Practice
1. If the speed of the object is halved (decreased by a factor of 2), the net force required is decreased by a
factor of 4.
2. If the speed of the object is doubled, the net force required for that object's circular motion is 4x.
3. A girl fills a bucket with water, ties it to a strong rope, and spins it in a circle. She spins the bucket when
it is half-full of water and when it is quarter-full of water. In which case is more force required to spin
the bucket in a circle? Explain. Half full means double the mass, so double the Fc
4. A Lincoln Continental and a Yugo are making a turn. The Lincoln is four times more massive than the
Yugo. If they make the turn at the same speed, then how do the centripetal forces acting upon the two
cars compare? Explain. Since  Fc  m, then 4*m, means 4*Fc
5. The Cajun Cliffhanger at Great America is a ride in which occupants line the perimeter of a cylinder and
spin in a circle at a high rate of turning. When the cylinder begins spinning very rapidly, the floor is
removed from under the riders' feet. What effect does a doubling in speed have upon the centripetal
force? Explain. Since  Fc  v2, then 2*v, means 4*Fc
6. If a 60-kg runner goes around a 20-m radius track at a rate of 2.5 m/s2, what is the centripetal force
necessary?
Fc = mac = 60* 2.5 = 150 N
7. A 3-kg wheel with a 12-cm radius rolls 0.75 m/s2. What is the centripetal force acting on the wheel?
Fc = mac = 3* 0.75 = 2.25 N
8. A 3-kg wheel with a 12-cm radius rolls with a speed of 0.13 m/s. What is the centripetal force?
Fc = m v2/R = 3 * 0.132/0.12 = 0.423 N
9. Determine the centripetal force acting upon a 40-kg child who makes 10 revolutions around the
Cliffhanger in 29.3 seconds. The radius of the barrel is 2.90 meters.
v = d/t = 2R/T = 2(2.9)/29.3 = 6 m/s
Fc = m v2/R = 40*6.22/2.9 = 533 N
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