Respuesta :
Answer: a) 4.05 m/s², b) 1.5625 rad, c) 37.5 rad/s, d) 10.125 m/s
Explanation:
a = linear acceleration =?
Radius of car tires (r) = 0.27m
Angular acceleration (α) = 15.0 rad/s²
a)
The relationship between angular and linear acceleration is given by the formulae below
a = αr
a = 15.0 × 0.270
a = 4.05 m/s²
b)
Recall that
θ = ωot + αt²/2
Where θ = angular displacement and ωo = initial angular velocity = 0 ( since the body starts from rest).
θ = αt²/2
θ = 15 × (2.5)²/2
θ = 3.125/2 = 1.5625 rad.
But angular displacement = number of oscillations / time taken
1.5625 = number of oscillations / 2.5
Number of oscillations = 1.5625× 2.5 = 3.91 rad.
c)
Recall that
ω = ωo + αt
But the body starts it motion from rest, hence ωo = 0
ω = 15× 2.50
ω = 37.5 rad/s.
d)
Linear velocity is related to angular velocity via the formulae below
v = ωr
v = 37.5 × 0.270
v = 10.125 m/s
Answer:
A) 4.05 m/s²
B) 7.46 revolutions
C) 37.5 rad/s
D) 10.125 m/s
Explanation:
A) Radius; r = 0.27m
Angular acceleration; α = 15 rad/s²
Now, the formula for linear acceleration is given by;
a = rα
Where r is radius and α is angular acceleration while a is linear acceleration.
Thus,
a = 0.27 x 15
a = 4.05 m/s²
B) First, Let's find the final velocity in rev/s using the equation of motion; V = u + αt
Where α is angular acceleration.
V = 0 + (15 x 2.5) = 37.5 rad/s
Now, we are calculating in revolutions, so let's convert the velocity to rev/s
1 rad/s = 1/2π rev/s
Thus, 37.5 rad/s = 37.5/2π revs/s = 5.968 rev/s
Now,average velocity = (v + u)/2 = (5.968 + 0)/2 = 5.968/2 = 2.984 revs/s
Thus, number of revolutions will be= average velocity x t =
2.984 rev/s x 2.5 s = 7.46 revolutions
C) we will get the final angular velocity from;
ω_f = ω_o + αt
Since it starts from rest, initial angular velocity ω_o = 0
Thus,
ω_f = 15 x 2.5 = 37.5 rad/s
D) The final velocity is given by;
v_f = ω_f•r = 37.5 x 0.27 = 10.125 m/s
