Physics Fundamentals | MCQs

Explanation

Explanation

The centripetal force (F) acting on the roller coaster is given by the formula:

F = (m × v^2) / r

Where:

m = net mass of coaster + passengers

v = velocity = 30 m/s

r = radius of the circular track = 30 m

Substituting the values, we get:

F = (m × (30)^2) / 30

= (m × 900) / 30

= 900m / 30

= 900m

So, the centripetal force acting on the roller coaster is 900m.

Explanation

Angular velocity (ω) is defined as the rate of change of angular displacement (θ) with respect to time (t). It can be calculated using the formula:

ω = v / r

Where:

v = linear velocity (in m/s)

r = radius of the circle (in m)

Given:

v = 250 m/s (linear velocity)

r = 100 m (radius of the circle)

ω = v / r

= 250 m/s / 100 m

= 2.5 rad/s

So, the angular velocity of the aircraft is 2.5 rad/sec.