CALC The angle θ through which a disk drive turns is given by θ (t) = a + bt − ct 3 , where a , b , and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π /4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s 2 , (a) Find a , b , and c , including their units, (b) What is the angular acceleration when θ = π/4 rad? (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s 2 ?
CALC The angle θ through which a disk drive turns is given by θ (t) = a + bt − ct 3 , where a , b , and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π /4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s 2 , (a) Find a , b , and c , including their units, (b) What is the angular acceleration when θ = π/4 rad? (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s 2 ?
CALC The angle θ through which a disk drive turns is given by θ (t) = a + bt − ct3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s2, (a) Find a, b, and c, including their units, (b) What is the angular acceleration when θ = π/4 rad? (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s2?
Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.
î
A proton is projected in the positive x direction into a region of uniform electric field E = (-5.50 x 105) i N/C at t = 0. The
proton travels 7.20 cm as it comes to rest.
(a) Determine the acceleration of the proton.
magnitude 5.27e13
direction -X
m/s²
(b) Determine the initial speed of the proton.
8.71e-6
magnitude The electric field is constant, so the force is constant, which means the acceleration will be constant.
m/s
direction +X
(c) Determine the time interval over which the proton comes to rest.
1.65e-7
Review you equations for constant accelerated motion. s
Three charged particles are at the corners of an equilateral triangle as shown in the figure below. (Let q = 2.00 μC, and
L = 0.750 m.)
y
7.00 με
60.0°
L
9
-4.00 μC
x
(a) Calculate the electric field at the position of charge q due to the 7.00-μC and -4.00-μC charges.
112
Once you calculate the magnitude of the field contribution from each charge you need to add these as vectors.
KN/CI + 64
×
Think carefully about the direction of the field due to the 7.00-μC charge. KN/Cĵ
(b) Use your answer to part (a) to determine the force on charge q.
240.0
If you know the electric field at a particular point, how do you find the force that acts on a charge at that point? mN
Î + 194.0
×
If you know the electric field at a particular point, how do you find the force that acts on a charge at that point? mN
In the Donkey Kong Country video games you often get around by shooting yourself out of barrel cannons. Donkey Kong wants to launch out of one barrel and land in a different one that is a distance in x of 9.28 m away. To do so he launches himself at a velocity of 22.6 m/s at an angle of 30.0°. At what height does the 2nd barrel need to be for Donkey Kong to land in it? (measure from the height of barrel 1, aka y0=0)
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