Explanation:
The linear analog of angle is angle itself.
The linear analog of angular velocity is linear velocity.
ω is angular velocity, therefore linear velocity is given by v
∴ for linear velocity, 
for angular velocity, 
The linear analog of angular acceleration is acceleration.
α is angular acceleration whereas as a is linear acceleration.
∴ for linear acceleration, v = u + a.t
for angular acceleration, 
The linear analog of moment of inertia is mass.
I is moment of inertia and m is mass,
∴ for linear analog, F = m.a
for angular analog, τ - I.α
Answer:
maximum speed of the bananas is 18.8183 m/s
Explanation:
Given data
amplitude A = 23.195 cm
spring constant K = 15.2676 N/m
mass of the bananas m = 56.9816 kg
to find out
maximum speed of the bananas
solution
we know that radial oscillation frequency formula that is = √(K/A)
radial oscillation frequency = √(15.2676/23.195)
radial oscillation frequency is 0.8113125 rad/s
so maximum speed of the bananas = radial oscillation frequency × amplitude
maximum speed of the bananas = 0.8113125 × 23.195
maximum speed of the bananas is 18.8183 m/s
Answer:
Explanation:
a) ωp = 2π radians / 1.7 s = <u>3.7 rad/s</u>
b) ωs = 3.7 rad/s(9.5 cm / 4.5 cm) = 7.8 rad/s
v = (ωs)R = 7.8(65) = 507 cm/s or <u>5.1 m/s</u>
c) ωs = 3.5 m/s / 0.65 m = 5.38 rad/s
ωp = 5.38(4.5 cm / 9.5 cm) = 2.55 rad/s
t = θ/ω = 2π / 2.55 = 2.463... <u>2.5 s</u>
Horizontal distance covered by a projectile is X = Vix *T
where Vix is the initial horizontal component of velocity and T is time taken by the projectile
Vix = ViCos theta
In question they said that initial velocity and angle is same on earth and moon
so Vix would remains same
now let's see about time taken T
time taken to reach the highest point
Vfy = Viy +gt
at highest point vertical velocity become zero so Vfy =0
0 = Vi Sin theta + gt
t = Vi Sintheta /g
Total time taken to land will be twice of that
On earth
Te= 2t
Te = 2Sinθ/g
on moon g is one-sixth of g(earth)
Tm = 2Sinθ/(g/6)
Tm = 6(2Sinθ/g)
Tm = 6Te
so total time taken by the projectile on moon will be six times the time taken on earth
From first equation X = Vix*T
we can see that X will also be 6 times on moon than earth
so projectile will cover 6 times distance on moon than on earth
