8/12/2019 H2 T7 Motion in a Circle Tutorial 09

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Tutorial 7 : Motion in a circle

1. A satellite moves at constant speed in a circular orbit around the Earth. State and explainwhether the following physical quantities of the satellite is constant or varying.(a) angular velocity

(b) linear velocity(c) linear momentum(d) acceleration(e) force(f) kinetic energy

(a) angular velocity (constant)Since the satellite is moving at a constant speed thus for a revolution around Earth thetime taken should be the same i.e. angular velocity should be constant (same magnitudeand direction)

(b) linear velocity (varying)

Since the direction of velocity is always changing the linear velocity is varying.

(c) linear momentum (varying)Since linear momentum is the product of mass and linear velocity the linear momentumis varying (with constant mass and varying linear velocity)

(d) acceleration (varying)Since the centripetal acceleration is always pointing towards the centre of circle thedirection of (centripetal) acceleration will be varying at different points of the circular path.!hus acceleration is varying.

(e) force (varying)

Since centripetal acceleration is varying at different points of the circular path thecentripetal force is varying too.

(f) kinetic energy (constant)Since kinetic energy only depends on the mass and the speed the kinetic energy of aconstant mass satellite with constant speed will be constant.

2. !he Singapore "lyer is #$% metres in diameter and makes one complete revolution in&% min. !here are ' capsules traveling with constant angular velocity.

(a) "ind the angle (in degrees and radian) subtended at the centre by two neighboringcapsules.

(b) "ind the angular velocity for the wheel.(c) "ind the linear velocity for the capsule.

(d) "ind the centripetal acceleration on one capsule.

8/12/2019 H2 T7 Motion in a Circle Tutorial 09

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(a) &*%o+ ' #'.,- %.'' rad

(b) & /#' ' &.$ #% rad s

&% *%T

= = =

(c) & /#0$ &., #% %.'*' m sv r = = =

(d)' '

. /'%.'*' ,.# #% m s0$

c

va

r

= = =

3. 1n the movie 22001: A Space Odyssey a rotating spacecraft pro/vides artificial gravity.

!he people would be walking inside the circle3 their feet toward the exterior and theirhead toward the center3 the floor and ceiling would curve upwards.

!he radius of the outer rim of the space 4wheel5 is #.% km.(i) 6alculate the angular velocity for the spacecraft to generate an artificial gequals to

,.# m s/'.(ii) 7hat is its equivalent no. of revolutions per min8

(i) ac= r 2= g

(#%%%) ' ,.# %.%,,% rad s

/#

(ii) = 2f%.%,,% = 2ff %.%#$ s/#

f %.%#$ 9 *% %.,* r.p.m.

4. :;*+1+$#+,