Answer on Question #51833-Physics-Other
1) A record turntable rotating at 34 rev/min slows down and stops in 30s after the motor is turned off
a) Find its (constant) angular acceleration in revolution per minute-squared
b) How many revolutions does it make in this time?
Solution
a) An angular acceleration is
rev
∆𝜔 𝜔 − 0 34 min
rev
𝛼=
=
=
= 68
.
∆𝑡
∆𝑡
0.5 𝑚𝑖𝑛
min2
b)
rev
𝛼∆𝑡 2
𝜔∆𝑡 𝜔∆𝑡 34 min ∙ 0.5 𝑚𝑖𝑛
𝑁 = 𝜔∆𝑡 −
= 𝜔∆𝑡 −
=
=
= 8.5 𝑟𝑒𝑣.
2
2
2
2
Answer: a) 𝟔𝟖
𝐫𝐞𝐯
𝐦𝐢𝐧𝟐
b) 𝟖. 𝟓.
2) A uniform solid ball rolls smoothly along a floor, then up a ramp inclined at 30.0^(o).It momentarily stops
when it has rolled 1.0m along the ramp. What was its initial speed?
Solution
According to the conservation of energy law:
𝐸𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 + 𝐸𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 = 𝐸𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 ,
where 𝐸𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 =
𝑚𝑣 2
2
is initial translational kinetic energy of the ball, 𝐸𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 =
𝐼𝜔2
2
is initial rotational
kinetic energy of the ball, 𝐸𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 = 𝑚𝑔ℎ = 𝑚𝑔𝑙 sin 30 is final gravitational potential energy of the ball.
For a solid ball:
2
𝐼 = 𝑚𝑟 2 ,
5
where 𝑚 is a mass of ball, 𝑟 is a radius of ball. So,
𝐸𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 =
𝐼𝜔2 1 2
𝑚𝑣 2
=
𝑚𝑟 2 𝜔2 =
.
2
25
5
Thus,
𝑚𝑣 2 𝑚𝑣 2
+
= 𝑚𝑔𝑙 sin 30.
2
5
7 2
1
𝑣 = 𝑔𝑙 ∙ .
10
2
The initial speed is
5𝑔𝑙
5 ∙ 9.8 ∙ 1.0
𝑚
𝑣=√
=√
= 2.6 .
7
7
𝑠
𝒎
Answer: 𝟐. 𝟔 𝒔 .
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