Vietnam National University, Ho Chi Minh City
AP PHYSICS I
Title:
INERTIA FORCE
CENTRIFUGAL FORCE
Instructor(s):
Vũ Hoàng Hải, HCMUT
Lê Tống Thiện Nhân, HCMUS
1
Theory
1.1
Inertia And Non-Inertia Frame Of References(FOR)
• Inertia FOR:
FOR without acceleration (e.g moving with constant velocity or stay at rest)
• Non-Inertia FOR:
FOR with acceleration
1.2
Inertia Force Centrifugal Force
• Inertia Force:
Is Imaginary Force that added into Non-Inertia FOR to ensure Newton’s Law validity
in Non-inertia For
• Centrifugal Force:
Is Inertia Force in rotational FOR. With acceleration is centripetal acceleration
1.3
Main formulas
• Inertia Force:
F⃗inertial = −m⃗aF OR
⃗a: the acceleration of the frame of reference.
Magnitude:
|F⃗inertial | = m|⃗aF OR |
• Centrifugal Force
F⃗centrifugal = −m⃗aF OR = −m⃗acentripetal
Magnitude:
|F⃗inertial | = m|⃗acentripetal | = m
v2
= mω 2 R
R
Vật Lý Đại Cương
2
Excercise
2.1
Free-Response Question
2.1.1
Type 1: Inertia Force
Please Solve These Question in 2 type Frame Of References
Problem 1: In an elevator, there is a spring scale. A person of mass m = 60 kg stands on
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the scale. Take g = 10 m/s . What is the reading on the scale in the following cases?
a) The elevator is at rest?
2
b) The elevator is moving downward with uniform acceleration a = 0.2 m/s ?
2
c) The elevator is moving downward while decelerating uniformly with a = 0.2 m/s ?
Problem 2: A person uses an elevator to lift 100 kg of coal from a mine shaft to the ground.
2
2
The elevator has an acceleration of 0.25 m/s . Take g = 10 m/s . What is the force exerted by
the elevator floor on the coal?
Problem 3: A steel cable can support a maximum load of 450 kg. It is used to lift another
object of mass 400 kg. What is the maximum acceleration that the object can have without
2
breaking the cable? Take g = 10 m/s .
Problem 4: A cable is used to pull a bridge of mass m up to the top of a pole standing on a
cart. When the cart moves, the cable makes an angle α = 30◦ with the vertical. Given m = 100 g,
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take g = 10 m/s . Find:
a) The acceleration of the cart?
b) The tension in the cable?
2.1.2
Centrifugal Force
Problem 5: A car of mass 1200 kg moves uniformly over a curved bridge (assume it is a circular
arc) with a speed of 36 km/h. Determine the normal force acting on the car at the highest point
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of the bridge. The radius of curvature of the bridge is 50 m. Take g = 10 m/s .
Problem 6: A driver must steer his car through the top of a hill shaped as an arc of a circle
with radius 250 m. What is the maximum speed the car can have at the top of the hill so that
the car still presses against the road surface?
Problem 7: A mass of 100 g is attached to a spring of length 20 cm, spring constant 100 N/m,
rotating uniformly in a horizontal plane. Calculate the number of revolutions per minute if the
spring is stretched by 2 cm.
Problem 8: A spring with natural length l0 = 24.3 cm and stiffness k = 100 N/m has one
end fixed at point O, which is attached to a horizontal bar T free to rotate about O. The other
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Vật Lý Đại Cương
end is attached to a small mass A of m = 100 g. Rod T passes through point A and can slide
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without friction relative to T . Take g = 10 m/s .
The rod rotates uniformly around a vertical axis Oy with angular velocity ω = 10 rad/s.
Determine the extension of the spring. Determine the direction and magnitude of the elastic
force acting on point O. Neglect the mass of the spring.
y
O
A
T
Problem 9: A disk of radius R = 10 cm rotates uniformly in a vertical plane. A point M
on the rim of the disk makes one revolution in 1.5 s. Find the acceleration of point M when it is
located:
a) At the highest point of the circular path?
b) At the lowest point of the circular path?
Problem 10: A circular disk of radius R = 10 cm rotates uniformly in a vertical plane,
passing through its center.
a) If the disk makes 1.5 revolutions per second, what is the linear velocity of a point located on
the rim of the disk?
b) A small object is placed on the disk. The coefficient of friction between the object and the disk
is µ = 0.1. For what values of the angular velocity ω will the object placed on the disk not slip
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outward, regardless of its position? Take g = 10 m/s .
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