Answer:

Explanation:
Torque is defined as the cross product between the position vector ( the lever arm vector connecting the origin to the point of force application) and the force vector.

Due to the definition of cross product, the magnitude of the torque is given by:

Where
is the angle between the force and lever arm vectors. So, the length of the lever arm (r) is minimun when
is equal to one, solving for r:

Answer:
the angular velocity of the carousel after the child has started running =

Explanation:
Given that
the mass of the child = m
The radius of the disc = R
moment of inertia I = 
change in time = 
By using the torque around the inertia ; we have:
T = I×∝
where
R×F = I × ∝
R×F =
∝
F =
∝
∝ =
( expression for angular angular acceleration)
The first equation of motion of rotating wheel can be expressed as :

where ;
∝ =
Then;


∴ the angular velocity of the carousel after the child has started running =

Answer:
The force generated by a single muscle fiber can be increased by increasing the frequency of action potentials
Explanation:
The force generated by a muscle fiber is the result of the shortening of the skeletal muscle, and this force is also know as muscle tension. The larger motor units shorten along with the smaller units to produce the muscle force. The time lapsed between the beginning of the action potential in the muscle and the beginning of the contraction is the latent period. Action potential is the result of the difference electrical potential as a result of passage of an impulse along the membrane of a muscle or nerve cell.
a. The restoring force in the spring has magnitude
F[spring] = k (0.79 m)
which counters the weight of the mass,
F[weight] = (0.46 kg) g = 4.508 N
so that by Newton's second law,
F[spring] - F[weight] = 0 ⇒ k = (4.508 N) / (0.79 m) ≈ 5.7 N/m
b. Using the same equation as before, we now have
F[weight] = (0.75 kg) g = 7.35 N
so that
(5.7 N/m) x - 7.35 N = 0 ⇒ x = (7.35 N) / (5.7 N/m) ≈ 1.3 m
Answer:
a = 1.5*10^-3 m/s^2
x = 0.033m = 3.3cm
Explanation:
To calculate the acceleration and the distance traveled by the car you use the following formulas:
(1)
(2)
v: final velocity = 0,255 km/h
vo: initial velocity = 0 m/s
t: time = 3/4 min
a: acceleration = ?
x: distance
In order to use the equations (1) and (2) you first convert the units of the final velocity to m/s, and the time to seconds.

Next, you solve the equation (1) for the acceleration a:

With this value of a you can calculate the distance traveled by the car, by using the equation (2):

hence, the acceleration of the car is 1.5*10^-3 m/s^2 and the distance traveled in 3/4 min is 0.033m