1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
RSB [31]
3 years ago
15

A wheel starts from rest and has an angular acceleration that is given by α (t) = (6.0 rad/s4)t2. After it has turned through 10

rev its angular velocity is:
Physics
1 answer:
marissa [1.9K]3 years ago
7 0

Answer:

75 rad/s

Explanation:

The angular acceleration is the time rate of change of angular velocity. It is given by the formula:

α(t) = d/dt[ω(t)]

Hence: ω(t) = ∫a(t) dt

Also, angular velocity is the time rate of change of displacement. It is given by:

ω(t) = d/dt[θ(t)]

θ(t) = ∫w(t) dt

θ(t) = ∫∫α(t) dtdt

Given that: α (t) = (6.0 rad/s4)t² = 6t² rad/s⁴. Hence:

θ(t) = ∫∫α(t) dtdt

θ(t) = ∫∫6t² dtdt =∫[∫6t² dt]dt

θ(t) = ∫[2t³]dt = t⁴/2 rad

θ(t) = t⁴/2 rad

At θ(t) = 10 rev = (10 *  2π) rad = 20π rad, we can find t:

20π = t⁴/2

40π = t⁴

t = ⁴√40π

t = 3.348 s

ω(t) = ∫α(t) dt = ∫6t² dt = 2t³

ω(t) = 2t³

ω(3.348) = 2(3.348)³ = 75 rad/s

You might be interested in
When the spacecraft is at the halfway point, how does the strength of the gravitional force on the spaceprobe by Earth compre wi
mixer [17]

Solution :

When the spacecraft is at halfway point, the distance from the Earth as well as Mars are same. We have to account the masses of the planets. The gravitational force that is exerted by the Earth is greater because of its combined mass with the space probe.

The mass of Earth is greater than the mass of Mars. Therefore, the force of Earth is more than Mars.

5 0
3 years ago
Cold air holds less water than warm air.<br> True<br> False
Vsevolod [243]

Answer:

The answer is for your question is :

Explanation:

True

4 0
2 years ago
You are standing a distance of 17.0 meters from the center of a merry-go-round. The merry-go-round takes 9.50 seconds to go comp
GenaCL600 [577]

Answer:

(a)11.24 m/s

(b)7.44 m/s

(c)409 N

(d)539.55\mu

(e) 0

Explanation:

The period for 1 circle 2\pi of the merry go around is 9.5s. It means the angular speed is:

\omega = \theta / t = 2\pi / 9.5 \approx 0.661 rad/s

(a)The speed is

v = \omega * R = 0.661 * 17 = 11.24 m/s

(b) Centripetal acceleration:

a = \frac{v^2}{R} = \frac{11.24^2}{17} = 7.44 m/s^2

(c) Magnitude of the force that keeps you go around at this acceleration

F = ma = 55 * 7.44 = 409 N

(d) let the coefficient of friction by \mu. The frictional force shall be this coefficient multiplied by normal force reverting gravity of the man

F_f = mg\mu = 55*9.81\mu = 539.55\mu

3 0
3 years ago
A generator converts mechanical energy into _____________________ energy.
erica [24]
Electrical energy is your answer.
6 0
3 years ago
Read 2 more answers
How long does it take a car travelling at 60 m.p.h to cover 5 miles?
k0ka [10]

Answer:

Time = 5 minutes

6 0
3 years ago
Read 2 more answers
Other questions:
  • The bending of light as it passes from one medium to the next is
    5·1 answer
  • What are 2 types of force fields
    6·1 answer
  • What happens when you break a magnet in half
    12·2 answers
  • a car travels 50 kilometers West and 10 minutes. after reaching the destination the car troubles back to the starting point, aga
    5·1 answer
  • WILL GIVE BRAINLIEST! THANK YOU :)
    5·1 answer
  • What is the rate of heat transfer by radiation, with an unclothed person standing in a dark room whose ambient temperature is 22
    15·1 answer
  • I need this question's answer lo long define rest <br>​
    6·1 answer
  • Will give brainliest!!
    13·2 answers
  • A circuit supplied with 110V carries 5 Amps current. Calculate the Resistance value of the circuit?
    11·1 answer
  • Draw a ray diagram for a diverging lens that has a focal length of -10 cm when an object is placed 30 cm from the lens's surface
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!