(a) 4.03 s
The initial angular velocity of the wheel is

The angular acceleration of the wheel is

negative since it is a deceleration.
The angular acceleration can be also written as

where
is the final angular velocity (the wheel comes to a stop)
t is the time it takes for the wheel to stop
Solving for t, we find

(b) 27.6 rad
The angular displacement of the wheel in angular accelerated motion is given by

where we have
is the initial angular velocity
is the angular acceleration
t = 4.03 s is the total time of the motion
Substituting numbers, we find

Most objects move at a constant speed because of friction and acceleration. The constant speed keeps them in place, and keeps a balance.
Answer:
The small pebble
Explanation:
Since the potential energy, P.E lost equals kinetic energy, K.E gained,
P.E = K.E
P.E = mgh = K.E
So, K.E = mgh where g = acceleration due to gravity and h = height of drop
Since h and g are constant
K.E ∝ m
So, the kinetic energy of the object is directly proportional to its mass. Thus, the object with the smaller mass has the lesser kinetic energy.
Since the object with the smaller mass is the small pebble, so the small pebble would have less kinetic energy as it crashes on the road at the bottom of the mountain.
Answer:
8.362m/s
Explanation:
Given data
Mass m1= 7.77kg
Velocity v1= 7.77m/s
Mass m2= 8.88kg
Velocity v2= 8.88m/s
Apply the law of conservation of momentum for inelastic collision we have
m1v1+m2v2= (m+m2)V
7.77*7.77+ 8.88*8.88= (7.77+8.88)V
60.3729+78.8544= 16.65V
139.2273= 16.65V
Divide both sides by 16.65
V= 139.2273/16.65
V= 8.362m/s
Hence the final velocity is 8.362m/s