Question

At the local carnival you and a friend decide to take a ride on the Ferris wheel. As the wheel rotates with a constant angular speed, your friend poses the following questions:

(a) Is my linear velocity constant?
(b) Is my linear speed constant?
(c) Is the magnitude of my centripetal accel-eration constant?
(d) Is the direction of my centripetal acceleration constant?
What is your an-swer to each of these questions?

Answer 1

A) No

B) Yes

C) Yes

D) Yes

Step-by-step explanation:

For a Ferris wheel with constant angular speed:

• The velocity of the system at its circumference constantly varies in its direction as the tangential direction is different at each point. If his friend is sitting on the same frame of reference then with respect to his friend his velocity is zero.

• Since the angular velocity is constant, the speed for a system at its circumference will remain constant in magnitude. If his friend is sitting on the same frame of reference then with respect to his friend his velocity is zero.

• We know that centripetal acceleration is given by:
• 
  `a_c=(v^2)/(r)` and in this case neither the radius of the system is varying nor the speed and also the center of rotation is fixed so we have the centripetal acceleration as constant in magnitude. While his friend being on the same frame of reference next to him will no centripetal acceleration with respect to him.

• The direction of centripetal acceleration will remain always towards the center of rotation of the wheel and the center remains fixed here. So with respect to his friend sitting on the same system his centripetal acceleration will always point in the same direction i.e. towards the center of the wheel.

Answer 2

a) No

b) Yes

c) Yes

d) Yes

Step-by-step explanation:

For a wheel with constant speed:

a) The velocity of the system at its circumference constantly varies. The tangential motion is different at each point of the motion.

b) Since the angular velocity is constant, the speed of the system at the circumference is constant.

c) First, we have to compute the centripetal acceleration which is given by the following formula:

`a_(c) = (v^(2) )/(r)`. In this case, the radius of the system is not varying and the speed is constant. Thus, the centripetal acceleration is constant.

d) The direction of the centripetal acceleration will remain the same towards the center of the rotation of the wheel.