Question

Questions on rotational motion? Any help would be appreciated because I don't understand any of it. Thanks!

1. A wheel rotates on a stationary axle. If its angular speed doubles, the centripetal acceleration of the rim will
a. quadruple
b. double
c. half
d. remain the same

2. What's the angular speed of a wheel that makes 50 revolutions in 10 seconds? Give answer in radians per second.
a. 10 seconds
b. 5 seconds
c. 5pi seconds
d. 10pi seconds

Answer 1

3. In a simple Atwood machine, the masses are released from rest and accelerate at a rate a. If the radius of the pulley is r, through what angle does the pulley rotate in time t after the masses are released?
a. ra/t
b. 2ra/t^2
c. a/rt
d. 2a/rt^2

4. If the net force of an object is directed perpendicular to its velocity,
a. the object is speeding up
b. the object is turning
c. the object is slowing down.
d. the object is not moving
e. this situation is not possible

5. An airplane is flying with constant speed of 300 m/s along a horizontal circle with a radius of 15,000 m. If the lift force of the air on the wings is perpendicular to the wings, at what angle relative to the horizontal should the wings be banked?
a. 22.2 degrees
b. 15.1 degrees
c. 31.5 dgrees
d. 37.7 degrees
e. 63 degrees

6. A 70 kg person's weight is normally 700 N. What is their apparent weight in a car going 10 m/s
through a dip with radius of curvature 10 m?
a. 350 N
b. 700 N
c. 1050 N
d. 1400 N
0 seconds ago - 4 days left to answ

Answer 2

1. centripetal acceleration is given by \[r \omega ^{2}\] where r is radius and omega is angular speed..
so when angular speed doubles centripetal acceleration quadruple

2. one rotation is equivalent to 2 pi radian.. and 50 rotation is equivalent to 100 pi radian.. sine the time taken is 10 sec.. the angular speed in radian per sec =(100 pi/10)radian per sec = 10 pi radian per second..

3. is angular acceleration equal to a or is it the linear acceleration?

4. the object is turning..
explanation: the component of force along the direction of velocity is zero.. so this force can't cause linear acceleration.. but it makes the body turn..

5. If L be the lift and theta be the angle made by airplane with horizontol then
\[L \cos \theta= mg....(1)\] \[L \sin \theta= mv ^{2}\div r.......(2)\] where m is mass of airplane
r is radius
v is velocity
so from above two relation \[\theta= \tan ^{-1}(v ^{2}\div rg)\]By calculation theta= 31.5 degrees

6. their apparent weight is equal to centripetal force given by
F=mv^2 /r
from above equation F is found to be 700 N.. so apparent weight is 700 N. (i guess)

P.S. I am not 100% sure about question no.6.. is the circle horizontal or verticle.. if its vertical, apparent weight changes every instant..

Answer 3

@ujjwal i think for #3 it is the angular acceleration

Answer 4

http://i43.tinypic.com/fy282d.png diagram for #6

Answer 5

answer for #6: 1400 N.. 700 N is the weight and 700 N is due to centrifugal force.. that makes a sum of 1400 N