Given:
Shaft Power, P = 7.46 kW = 7460 W
Speed, N = 1200 rpm
Shearing stress of shaft,
= 30 MPa
Shearing stress of key,
= 240 MPa
width of key, w = 
d is shaft diameter
Solution:
Torque, T = 
where,

= 59.365 N-m
Now,


d = 0.0216 m
Now,
w =
=
= 5.4 mm
Now, for shear stress in key
= 
we know that
T =
= F. 
⇒
= 
⇒
= 
length of the rectangular key, l = 4.078 mm
Answer:
70 cm
Explanation:
0.5 kg at 20 cm
0.3 kg at 60 cm
x = Distance of the third 0.6 kg mass
Meter stick hanging at 50 cm
Torque about the support point is given by (torque is conserved)

The position of the third mass of 0.6 kg is at 20+50 = 70 cm
Answer:
1) τ = I α whereby the torque is provided by the angular acceleration
2) L = 216 Kg m² / s
Explanation:
1) Let's start with Newton's second law
F = m a
multiply by the arm or perpendicular distance
F r = m a r
if the distance is not perpendicular a way of realizing the relations using the vector product
τ = F r = F x r
the bold are vectors. The angular and linear acceleration are related
a = α r=
τ = m (α r) r
τ = (m r²) α
the inertia of the rotational motion is
I = m r²
we substitute
τ = I α
whereby the torque is provided by the angular acceleration.
As an example we have:
* a spinning disk
* a ball rotating in the air
* a pulley
2) The rotational momentum is
L = I w
the moment of inertia of a rod that through its center
I = m L²
we substitute
L = m L² w
let's calculate
L = 6 1.5 2 16
L = 216 Kg m² / s
Answer:
When a an object is been rotated its resistance capacity to that rotational force is know as rotational inertia and this mathematically given as

Where m is the mass
r is the rotation radius
For the spinning of the lamp as a baton to work the location of the center of mass of the floor lamp needs to be located
This is more likely to be located closer to base of the lamp as compared to the top, so success of spinning a floor lamp like a baton is highly likely if the lamp is grabbed closer to the base because that is where the position of its center of mass is likely to be.
Explanation:
Answer:
(a) Rm = 268.4 m
(b) f = 6
Explanation:
The horizontal range of a projectile is given by the following formula:
R = V₀² Sin 2θ/g
(a)
For moon:
R = Range on moon = Rm
V₀ = Launch Speed = 28 m/s
θ = Launch Angle = 17°
g = acceleration due to gravity on moon = (9.8 m/s²)/6 = 1.63 m/s²
Therefore,
Rm = (28 m/s)²Sin (2*17°)/(1.63 m/s²)
<u>Rm = 268.4 m</u>
(b)
For Earth:
R = Range on Earth = Re
V₀ = Launch Speed = 28 m/s
θ = Launch Angle = 17°
g = acceleration due to gravity on Earth = 9.8 m/s²
Therefore,
Re = (28 m/s)²Sin (2*17°)/(9.8 m/s²)
Re = 44.7 m
Therefore.
f = Rm/Re = 268.4 m/44.7 m
<u>f = 6</u>