Answer all of them pls. Thank you. A Bicycle wheel is mounted on a fixed, fricti

Question

Answer all of them pls. Thank you.

A Bicycle wheel is mounted on a fixed, frictionless axle. A light string, is wound around the wheel's rim, and a weight is attached to the string at its free end. The diagrams below depict the situation at three different instances:

At t=t0, the weight is released from rest.

At t=t1, the weight is falling and the string is still partially wound around the wheel.

At t=t2, the weight and string have both reached the ground.

Note that the above diagrams do not represent stroboscopic photographs of the wheel.

Explanation / Answer

Part A

a) Angular velocity is in clockwise direction at t = t1 and t = t2 . Angular velocity is zero at t = to

b) Angular acceleration is in clockwise direction at t = to and t = t1 . Angular velocity is zero at t = t2

c) Centripetal acceleration = m2r

So, aA,2 > aA,1 > aA,o = 0

Part B

let a be the angular acceleration
let aR be the centripetal acceleration

Question 1:

the turntable is at rest
a = 0 implies there is no angular acceleration of theclay (ie. if the turntable were moving it would move at constantangular velocity)

aR = 0 implies there is no centripetal acceleration of the clay,but centripetal force on the clay is required if the turntable ismoving in circular motion
since the clay is stuck on the turntable, its motion must berepresentative of the turntable's motion.
thus the turntable is at rest

Question 2:

the turntable is rotating at a constant angular speed
again, a = 0 implies no angular acceleration of theclay (see above for explanation

this time, a non-zero aR implies there is a centripetal forceacting on the clay, which means that v is non-zero
since the clay is stuck on the turntable, its motion must berepresentative of the turntable's motion. Thus if there is noangular acceleration, but non-zero velocity, the turntable must bemoving at constant angular speed

Question 3:

the turntable is rotating but getting faster (or slower) as itturns
non-zero a implies the clay is experiencing non-zeroangular accelerating, which means it can either be slowing down orspeeding up, depending on if the accelerating is positive ornegative

non-zero centripetal force just means that the clay is moving innon-uniform circular motion (ie. its speed is no constant)
it follows that the turntable's motion is as describedabove.

Question 4:

aR/r is not a correct vector equation because no direction isspecified

Question 5:

since no direction is required for a scalar equation, then thatequation is valid if the left and right side have the sameunits
    assuming R and r do have the same units, thenthat is a correct scalar equation.

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