2010 Pearson Education, Inc. DoDEA – Physics (SPC 501) - Standards Pb.9 – Explain how torque ( ) is affected by the magnitude (F) , direction(Sin θ ) , and point of application of force ( R ) . = R*F(Sin θ) R = Torque Arm = distance between applied force and pivot point R = Torque Arm = distance between applied force and pivot point Pb.10 – Explain the relationships among speed , velocity , acceleration , and force in rotational systems. http://www.physicsclassroom.com/mmedia/circmot/ circmotTOC.html
DoDEA – Physics (SPC 501) - Standards. Pb.9 – Explain how torque ( ) is affected by the magnitude (F) , direction(Sin θ ) , and point of application of force ( R ) . = R* F(Sin θ ) R = Torque Arm = distance between applied force and pivot point - PowerPoint PPT Presentation
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A ladybug sits halfway between the rotational axis and the outer edge of the turntable . When the turntable has a rotational speed of 20 RPM and the bug has a tangential speed of 2 cm/s, what will be the rotational and tangential speeds of her friend who sits at the outer edge?
A ladybug sits halfway between the rotational axis and the outer edge of the turntable . When the turntable has a rotational speed of 20 RPM and the bug has a tangential speed of 2 cm/s, what will be the rotational and tangential speeds of her friend who sits at the outer edge?
A. 1 cm/sB. 2 cm/s C. 4 cm/sD. 8 cm/s
Rotational and Tangential Speed
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--Rotational speed () of both bugs is the same (20 RPM)--So if the radial distance (r) doubles, tangential speed (v) will also double.--Tangential speed (v) is 2 cm/s 2 = 4 cm/s.
In circular motion, the direction of any “point” is constantly changing. Therefore, the velocity (speed with direction) is also constantly changing.v1 v2 A change in direction
= A change in velocity= Acceleration a = Δv/t
Acceleration only occurs when there is a net force applied to an object a = F/m
In In which direction which direction must the FORCE be applied must the FORCE be applied in order for an object to continue to travel in in order for an object to continue to travel in constant circular motion? constant circular motion?
Direction of Force Direction of Force = = Direction of AccelerationDirection of Acceleration
Centripetal Acceleration (Ac) – Acceleration directed toward the center of a circular path --Always points toward center of circle. --(Centripetal = center seeking) --Always changing direction!
NOTENOTE: Velocity is always in a : Velocity is always in a straight linestraight line..
• Any force directed toward a fixed center is called a centripetal force (Fc). The magnitude of the force required to maintain uniform circular motion.
Example: To whirl a tin can at the end of a string, you pull the string toward the center and exert a centripetal force to keep the can moving in a circle.
Acceleration only occurs when there is a net force applied to an object a = F/m
Suppose you double the speed (v) at which you round a bend in the curve, by what factor must the centripetal force (Fc) change to prevent you from skidding?
A. DoubleB. Four times C. HalfD. One-quarter
Centripetal Force
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Explanation:
Because the term for “tangential speed” is squared, if you double the tangential speed, the centripetal force will be double squared, which is four times. The radius is constant.
l
2
radius
speed tangentialmass forceCentripeta
WARNINGWARNING: If you make a turn at : If you make a turn at double the speed, you are double the speed, you are 4 times4 times more more
likely to skid off of the road.likely to skid off of the road.
Suppose you take a sharper turn than before and halve the radius; by what factor will the centripetal force need to change to prevent skidding?
A. DoubleB. Four timesC. HalfD. One-quarter
Centripetal ForceCHECK YOUR ANSWER
Because the term for “radius” is in the denominator, if you halve the radius, the centripetal force will double.
WARNINGWARNING: The sharper your turn : The sharper your turn (smaller radius), the MORE likely you are (smaller radius), the MORE likely you are
to skid. The wider your turn (larger to skid. The wider your turn (larger radius), the LESS likely you are to skid.radius), the LESS likely you are to skid.
The cork will ONLY move while experiencing a net force (resulting in an acceleration). If I were to walk at a constant velocity, the cork would stay in the center.
A tube is been placed upon the table and shaped into a three-quarters circle. A golf ball is pushed into the tube at one end at high speed. The ball rolls through the tube and exits at the opposite end. Describe the path of the golf ball as it exits the tube.
Centripetal force is NOT a new “force”. It is simply a way of quantifying the magnitude of the force required to maintain a certain speed around a circular path of a certain radius.
Suppose two identical objects go around in horizontal circles of identical diameter but one object goes around the circle twice as fast as the other. The force required to keep the faster object on the circular path is _____ the force required to keep the slower object on the path.
Suppose two identical objects go around in horizontal circles with the same speed. The diameter of one circle is half of the diameter of the other. The force required to keep the object on the smaller circular path is ___ the force required to keep the object on the larger path.
A. the same as B. one fourth of C. half of D. twice E. four times
The answer is D. The centripetal force needed to maintain the circular motion of an object is inversely proportional to the radius of the circle. Everybody knows that it is harder to navigate a sharp turn than a wide turn.
Suppose two identical objects go around in horizontal circles of identical diameter and speed but one object has twice the mass of the other. The force required to keep the more massive object on the circular path is
A. the same as
B. one fourth of
C. half of
D. twice
E. four times
Answer: D.The mass is directly proportional to centripetal force.
The Normal Force Can Yield a Centripetal Acceleration:
How many forces are acting on How many forces are acting on the car (assuming no friction)?the car (assuming no friction)?
Engineers have learned to “bank” curves so that cars can safely travel around the curve without relying on friction at all to supply the centripetal acceleration.
Banked CurvesWhy exit ramps in highways are banked?
FN cos = mg
Fc = FN sin = mv2/r
The steeper the bank (, the less friction is needed (more Force Normal is applied toward the center). This is why/how a race car track can allow cars to travel at such high speeds.
The ride starts to spin faster and faster and you FEEL yourself being pushed back against the metal cage. Even when the ride starts to tilt skyward and you are looking
DOWN at the ground, still you feel yourself almost “forced” back so that you do NOT fall to your death. EXPLAIN….
An inward net force is required to make a turn in a circle. This inward net force requirement is known as a centripetal force requirement. In the absence of any net force, an object in motion (such as the passenger) continues in motion in a straight line at constant speed. This is Newton's first law of motion. While the car begins to make the turn, the passenger and the seat begin to edge rightward. In a sense, the car is beginning to slide out from under the passenger. Once striking the driver, the passenger can now turn with the car and experience some circle-like motion. There is never any outward force exerted upon the passenger. The passenger is either moving straight ahead in the absence of a force or moving along a circular path in the presence of an inward-directed force.
This path is an inward force - a centripetal force. That is spelled c-e-n-t-r-i-p-e-t-a-l, with a "p." The other word - centrifugal, with an "f" - will be considered our forbidden F-word. Simply don't use it and please don't believe in it.
A hoop and a disk are released from the top of an incline at the same time. Which one will reach the bottom first?A. HoopB. Disk C. Both togetherD. Not enough information
Rotational Inertia
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Explanation:Hoop has larger rotational inertia, so it will be slower in gaining speed.
Suppose the girl on the left suddenly is handed a bag of apples weighing 50 N. Where should she sit in order to balance, assuming the boy does not move? A. 1 m from pivotB. 1.5 m from pivotC. 2 m from pivotD. 2.5 m from pivot
Rotational Inertia
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Explanation:She should exert same torque as before.Torque lever arm force
3 m 250 N 750 Nm
Torque new lever arm force750 Nm new lever arm 250N New lever arm 750 Nm / 250 N 2.5 m
Suppose by pulling the weights in, if the rotational inertia of the man decreases to half of his initial rotational inertia, by what factor would his angular velocity change?
A. DoubleB. Three timesC. HalfD. One-quarter
Angular MomentumCHECK YOUR ANSWER
Explanation:
Angular momentum is proportional to “rotational inertia”.
If you halve the rotational inertia, to keep the angular momentum constant, the angular velocity would double.