If we neglect frictional force, the total mechanical energy of the ball is conserved.
The total mechanical energy of the ball is the sum of its kinetic energy K and its potential energy U:

where the kinetic energy depends on the speed v of the ball:
while the potential energy depends on the height h at which the ball is:

As the ball travels along the roller coaster, there is a continuous conversion between kinetic and potential energy, because the total mechanical energy E has always the same value. Therefore, when the ball goes on top of a hill, its height h increases and its potential energy U increases as well, while the speed v decreases and K decreases. Vice-versa, when the ball reaches the bottom of a hill, its height h decreases and therefore the potential energy U decreases, while the speed v increases and therefore the kinetic energy K of the ball increases as well.
Answer:
True; ar = v^2 / R Radial acceleration because it moves in a circular path
at = α R = tangential acceleration because its speed changes
a = at + ar total acceleration equals sum of radial and tangential
Answer:
The decided by staring at and observing the stars.
Explanation:
A because the toaster converts electrical energy into heat energy and, after the bread has been heated for sufficient time, toasts pop out, ready to be buttered. And converting means transforming.
(A) 
The energy stored by the system is given by

where
P is the power provided
t is the time elapsed
In this case, we have
P = 60 kW = 60,000 W is the power
t = 7 is the time
Therefore, the energy stored by the system is

(B) 4830 rad/s
The rotational energy of the wheel is given by
(1)
where
is the moment of inertia
is the angular velocity
The moment of inertia of the wheel is

where M is the mass and R the radius of the wheel.
We also know that the energy provided is

So we can rearrange eq.(1) to find the angular velocity:

(C) 
The centripetal acceleration of a point on the edge is given by

where
is the angular velocity
R = 0.12 m is the radius of the wheel
Substituting, we find
