Question

Consider an object on a rotating disk a distance r from its center, held in place on the disk by static friction. Which of the following statements is not true concerning this object:

A) If the angular speed is constant, the object must have constant tangenial speed.
B) If the angular speed is constant, the object is not accelerated
C) The object has a tangenial acceleration only if the disk has an angular acceleration.
D) If the disk has an angular acceleration, the object hasboth a centripetal and a tangenial acceleration
E) The object always has a centripetal acceleration exceptwhen the angular speed is zero

Answer 1

An object on a rotating disk experiences centripetal acceleration even at a constant angular speed. Centripetal acceleration is necessary for circular motion and is different from tangential acceleration, which occurs only when there is a change in the disk's angular speed. So the correct option is B.

Step-by-step explanation:

Among the given statements about an object on a rotating disk held in place by static friction, the statement that is not true is: B) If the angular speed is constant, the object is not accelerated. This is because even if the angular speed (ω) is constant, the object is still experiencing a constant centripetal acceleration towards the center of the disk, which is necessary to keep it moving in a circular path. However, it won't have tangential acceleration unless the angular speed of the disk changes.

Tangential acceleration occurs only when there is a change in the magnitude of the velocity - which requires a change in the angular speed of the disk. Centripetal acceleration, on the other hand, is always present in circular motion unless the object is not moving (angular speed is zero). It changes the direction of the velocity but not its magnitude.

When the disk's angular velocity is constant (uniform circular motion), the tangential speed remains the same since it depends on the product of the angular velocity and radius (v = rω). However, if the disk starts or stops spinning or changes its spinning rate (angular acceleration), the object will experience both centripetal and tangential accelerations.

Answer 2

A) False

B) False

C) True

D) True

E) True

Step-by-step explanation:

A) The formula for tangential speed v in term of angular speed ω and radius of rotation r is

`v = \omega r`

So if the angular speed is constant and 0, the tangential speed is also 0. A) is false

B) False because of the centripetal acceleration:

`a_c = \omega^2 r`

C) True because of the formula for tangential acceleration in term of angular acceleration α is

`a_t = \alpha r`

D) True because same as D), if it has angular acceleration, it would have a tangential acceleration. Also from B) the centripetal acceleration will come with time as soon as angular speed is generated by angular acceleration.

E) True and same explanation as from B)