1. Bung on a String with a partner work out the forces acting on the bung - what happens to the bung when you release it at each point around the circle?

2. Uniform Circular Motion – motion of an object in a circle with constant speed (constantly changing direction)
- Net force towards center (centripetal force)

3. 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦= 𝜔= Δθ Δ𝑡
𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛= 𝛼= Δ𝜔 Δ𝑡

4. The wheel on a car rotates with an angular acceleration of 10 r/s2
The wheel on a car rotates with an angular acceleration of 10 r/s2. If the wheel starts from 20 r/s, then… a) How fast will it be traveling after 20 seconds? b) How many rotations will the wheel have under gone? c) If the wheel’s radius is 35 cm, then what linear distance will the car have traveled?
a) 220 r/s b) rotations c) m

5. An ice skater spins on one skate
An ice skater spins on one skate. If she starts with an angular velocity of zero and end up with an angular velocity of 10 r/s in 1 second, then … a) What is her angular acceleration? b) How many rotations did she under go in reaching 10 r/s? c) How long will it take for her to spin 50 times?
a) 10r/s2 b) 0.8 rotations c) 31.9 sec

6. 𝑣 𝑇 = 2𝜋𝑟 𝑇
𝑣 𝑇 =𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 [ 𝑚 𝑠 ]
𝑎 𝑐 = 2𝜋 𝑣 𝑇 𝑇
𝑎 𝑐 =𝑐𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 [ 𝑚 𝑠 2 ]
𝑎 𝑐 = 𝑣 𝑇 2 𝑇
𝑟=𝑟𝑎𝑑𝑖𝑢𝑠 [𝑚]
𝐹 𝑐 =𝑐𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 [𝑁]
𝑎 𝑐 = 4 𝜋 2 𝑟 𝑇 2
𝑇=𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛 [𝑠]
𝐹 𝑐 =𝑚 𝑎 𝑐

7. ….Dimensional analysis….
Definitions (mathematical)
360° = 2π radians
1 revolution = 360°
1 revolution = 2π radians
1 revolution = 1 cycle
1 cycle = 360° = 2π radians
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦= # 𝑜𝑓 𝐶𝑦𝑐𝑙𝑒𝑠 𝑇𝑖𝑚𝑒
𝑝𝑒𝑟𝑖𝑜𝑑= 𝑇𝑖𝑚𝑒 # 𝑜𝑓 𝐶𝑦𝑐𝑙𝑒𝑠
𝑅𝑃𝑀= 𝑅𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 𝑀𝑖𝑛𝑢𝑡𝑒

8. A plane flies in a horizontal circle
A plane flies in a horizontal circle. If the plane turns with twice the centripetal acceleration and 3 times the speed then how does the new period of motion compare to the old?

9. A rock is twirled around in a horizontal circle overhead
A rock is twirled around in a horizontal circle overhead. The centripetal force applied to the string is doubled and the period is halved while the rock’s mass remains unchanged. By what factor did the radius change?

10. A turntable rotates an album at 33 revolutions per minute, RPM
A turntable rotates an album at 33 revolutions per minute, RPM. What frequency is this? HINT: frequency = 1/T NOTE: use SI units (Hz)

11. Middle “c” on the musical scale has a frequency of 256 Hz
Middle “c” on the musical scale has a frequency of 256 Hz. How many times a second is the sound wave vibrating?

12. When traveling down the road at a constant speed of 24
When traveling down the road at a constant speed of 24.6 m/s, the tangential velocity of the wheels is also 24.6 m/s. If a car’s tire is 65.0 cm in diameter, then; - What is the period and frequency of the spinning car tire? What is the centripetal acceleration of a rock stuck in the tire’s tread?

13. Given that the Earth is 1. 49 x 10^11 m from the Sun
Given that the Earth is 1.49 x 10^11 m from the Sun. And the Earth’s period of motion is days. Calculate how fast it is revolving around the Sun. Put your answer in m/s.

14. Do the same thing for the Moon: Given it is 3
Do the same thing for the Moon: Given it is 3.8 x 10^8 m from the Earth and revolves around the Earth every days. Put your answer in m/s.