PHYS 100 Chapter Notes - Chapter 6: Angular Velocity, Centripetal Force, Fictitious Force
10 May 2018
School
Department
Course
Professor
Chapter 6
- Rotation Angle and Angular Velocity
o Rotation Angle
▪ Each point of a circular object
follows a circular arc
▪ Rotational angle is defined as
the ratio of the arc length to the
radius of curvature
• Δ θ = Δs/r
• Arc length Δx is the distance traveled along a circular path
• R is the radius of curvature
• Circumference of a circle is 2 πr
• Δ θ = 2πr/r =2π
o 2π Rad = 1 Revolution
o Example:
▪ If Δθ = 2π
• 2π rad = 360
• 1 rad = 360/2π = 57.3
o Angular Velocity
▪ Defined as the rate of change of an angle
• W = Δθ/ΔT
▪ The greater the rotation angle in a given amount of time, the greater the
angular velocity
• rad/s
▪ This pit moves an arc length Δs in a time Δt, and so it has a linear velocity
• V = Δs/ Δt
▪ Δs = rΔθ
• V = rw
• W = v/r
▪ v is defined as linear velocity
• proportional to the distance from the center of rotation
• Faster the car moves, the faster the tire spins
o Large v means a large w
o Larger the radius tire rotating at the same angular velocity
(w) will produce a greater linear speed (v) for the car
▪ Example: Calculate the angular velocity of a 0.300m radius car tire when
the car travels 15.0m/s (54km/h)
• V = 15m/s
• R = 0.300m
• W = ?
• W = (15m/s)/(0.300m) = 50.0 rad/s
Centripetal Acceleration
- Ac (Centripetal Acceleration)
o Toward t he center
find more resources at oneclass.com
find more resources at oneclass.com
o The direction of centripetal acceleration is toward the center of curvature
o The magnitude of the centripetal acceleration is formulated as
▪ Ac = V2/r2 or Ac = rw2
• Acceleration of an objective in a circle of radius (r) at a speed (v)
• Centripetal acceleration is greater at high speeds and in sharp
curves
o Example: What is the magnitude of centripetal acceleration of a car following a
curve of radius 500m at the speed of 25m/s
▪ V = 25m/s
▪ R = 500m
▪ Ac = v2/r
• (25m/s)2/500m
• 1.25m/s2
o Example: Calculate the Centripetal Accelation of a point 7.5cm from the axis of a
centrifuge spinning at 7.5x104 rev/min
▪ (7.5x104rev/min)*(2π rad/1rev)*(1min/60s)
• 7854rad/s
▪ Ac = rw2
• (0.075m)(7854rad/s)2 = 4.63x106 m/s2
Centripetal Force
- Net force causing circular motion
- A = F/m
o A = Centripetal acceleration
o F = centripetal force
o AC = V2/R
▪ V = constant speed
▪ R = Radius
o A = ∑F / m
▪ AC = ∑F / M
▪ Ac = v2/r
▪ V2 / R = FC / M
▪ FT = m (v2 / r) – Force Tension
o V2 / r = ∑Fc / M
▪ V2 / r = mg – FN / m
▪ FN = mg – m (v2 / r)
- Toward the center curvature, same direction as the director of centripetal acceleration
o Net force is mass times acceleration
o FC = mac
▪ Fc = mrw2
▪ Fc is always perpendicular to the path and pointing to the center of
curvature, because Ac is perpendicular to the velocity and pointing to the
center of curvature
• R = mv2/Fc
o Example: Calculate the centripetal force on a 900kg car that negotiates a 500m
radius at a curvhe at 25m/s
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
65degrees tan = v2/rg: v = (rg tan )1/2, tan = tan65, (100m)(9. 80m/s2)(2. 14)1/2, 45. 8m/s. Car is a non-intertial frame of reference because it is accelerated to the side: force to the left is fictitious force having no physical origin. Centrifugal force: force that acts outward on a body moving around a center, from the body"s inertia. Universal law of gravitation states that every particle in the universe attracts every other particle with a force along joining them. Microgravity and weightlessness: microgravity refers to an environment in which the apparent net acceleration of a body is small compared with that produced by the earth at its surface. A small mass (m) orbits a larger mass m: allows us to view the motion as if m were stationary. The system is isolated from other masses. 2)= (r3: t is the orbital period, r is the average orbital radius.
