Rotation angle and ω
The minute hand of a clock moves from 12 to 9 in a 45-minute period. How far does it move (in radians)?
0.75*2𝞹 = 4.71 rad
Provided you are traveling with the same (linear) speed around a curve, will your centripital acceleration increase or decrease if the radius of the curve decreases
Your centripital acceleration will increase
On a merry-go-round, is the centripetal force greater towards the inside of the carousel, or towards the outside?
If the mass of two objects is tripled, what happens to the magnitude of the gravitational force between them?
True or false: Kepler's laws only apply to planets orbiting the sun.
False, Kepler's laws apply to all orbiting objects
The minute hand of a clock is 0.1m long. How far does the tip of the minute hand travel in a full hour?
2𝞹*0.1 = 0.63m
A race car drives 88.9 m/s arround the Indy500 track, which has a radius curvature of 250m. What is the car's centripital acceleration?
31.6 rad/s
A 75kg person is spun arround in a carnival machine at 13 m/s. If they are positioned 3.0m from the center of rotation, what centripital force do they experience?
4225N
What happens to the gravitational force between two objects if the distance between them is tripled?
It will be 1/9 th of its initial value
What is Kepler's first law?
All planets move in elliptical orbits with the sun at one focus
When rolling down a hill, the wheels of a skateboard rotate at 1800 rev/min. What is the angular velocity of the skateboard wheel?
1800*2𝞹*(1/60) = 188 rad/s
How does your linear velocity change (it at all) when moving from the center of a carosel to the outer rim? How does your angular velocity change (it at all) when making the same move?
Your linear velocity will increase.
Your angular velocity will remain constant.
You put a can of soup in a grocery bag before spinning it vertically around your wrist. Why does the soup not fall out, even when the bag is upsidown?
The can's inertia keeps it moving in a straight line (into the bag). When the bag moves, the can being pushed into it will follow its bath.
Why is there an apparent lack of gravity of the Internatonal Space Station?
The ISS is moving fast enough as to be orbiting/ free falling around the Earth. When in free fall, the lack of a normal force creates a feeling of weightlessness, and the illusion of zero-gravity.
Does a planet orbiting the sun move faster when it is closer to the sun, or when it is further away? Draw a diagram to support your answer.
Closer to the sun (it will cover a create distance in the same amount of time)
A cowboy spins his lasso above his head at 8.81 rad/s. How long does it take the lasso to make one full rotation?
ω=θ/t
8.81=2𝞹/t
t=0.71 s
Your centripital acceleration is 4m/s2 while running in a circle at 1.88 rad/s. What is the radius of the circle you are running in?
ac=rω2
1.13m
A 0.05kg spinning top rotates at 40 rev/s. If the spinning top measures 0.02m across, what is the centripital force experience on the outer most part of the top?
31.6N
*r=0.01m, 40 rev/s=251.3 rad/s
What is the gravitational force between two 19kg desks when they are 0.85m apart?
3.33*10-8 N
Moon X has an orbital period (arround a planet) that is 4 times as long as moon Z. How many times further away is moon X?
= 2.52 times as far
A 0.64 meter baton is twirled at 17m/s. What is the baton's angular velocity?
17/0.32 = 53.1 rad/s
A record player (r=30cm) spins at 45 rotations per minute. What is the angular acceleration on the edge of the record?
6.66 m/s2
ac=rω2
ac=0.3*(45*2 𝞹*1/60)2
A 0.25 kg teatherball spins arround a pole, attached to a rope that is 1.8m long. If this causes the teatherball to experience a centripital force of 310N, what is the ball's angular velocity?
Fc=mrω2
26.2 rad/s
Calculate the acceleration due to gravity on Earth, due to the moon when the moon is 3.84*108 m away.
mmoon= 7.35*1022 kg
3.33*10-5 m/s2
Earth is (on average) 1.47*108 km from the sun. If Venus is 1.09*108 km, what is its orbital period in Earth years?
0.639 Earth years