Answer:
a) θ = 2500 radians
b) α = 200 rad/s²
Explanation:
Using equations of motion,
θ = (w - w₀)t/2
θ = angle turned through = ?
w = final angular velocity = 1420 rad/s
w₀ = initial angular velocity = 420
t = time taken = 5s
θ = (1420 - 420) × 5/2 = 2500 rads
Again,
w = w₀ + αt
α = angular accelaration = ?
1420 = 420 + 5α
α = 1000/5 = 200 rad/s²
To develop this problem it is necessary to apply the concepts given in the balance of forces for the tangential force and the centripetal force. An easy way to detail this problem is through a free body diagram that describes the behavior of the body and the forces to which it is subject.
PART A) Normal Force.


Here,
Normal reaction of the ring is N and velocity of the ring is v




PART B) Acceleration





Negative symbol indicates deceleration.
<em>NOTE: For the problem, the graph in which the turning radius and the angle of suspension was specified was not supplied. A graphic that matches the description given by the problem is attached.</em>
Answer:
17.64 km/h
Explanation:
mass of car, m = 1000 kg
Kinetic energy of car, K = 1.2 x 10^4 J
Let the speed of car is v.
Use the formula for kinetic energy.

By substituting the values

v = 4.9 m/s
Now convert metre per second into km / h
We know that
1 km = 1000 m
1 h = 3600 second
So, 
v = 17.64 km/h
Thus, the reading of speedometer is 17.64 km/h.
∑F = ma = (90 kg)(1.2 m/s²) = 108 N = 100 N (1 significant digit)