A pulsar is a rapidly rotating neutron star. The Crab Pulsar is located in the C

Question

A pulsar is a rapidly rotating neutron star. The Crab Pulsar is located in the Crab Nebula in the constellation Taurus. The pulsar is in the center of the close-up view of the nebula shown in the photograph. The periods of pulsars can be measured with great accuracy: The Crab Pulsar has a period of 0.033 s. (a) Find the pulsar's angular velocity. (b) The radius of the pulsar is estimated to be 10 km. Find the tangential velocity of a point on its equator.

A model train runs on a circular track with radius 1.2 m. Its tangential velocity is 1.2 m/s and it is accelerating with a tangential acceleration of 0.90 m/s2. What is the magnitude of the train’s overall acceleration? Find the angle between the overall acceleration and the centripetal acceleration.

A flywheel has a constant angular acceleration of 0.81 rad/s2. What is its angular velocity 14 s after its angular velocity is 4.8 rad/s?

A pulsar is a rapidly rotating neutron star. The Crab Pulsar is located in the Crab Nebula in the constellation Taurus. The pulsar is in the center of the close-up view of the nebula shown in the photograph. The periods of pulsars can be measured with great accuracy: The Crab Pulsar has a period of 0.033 s. (a) Find the pulsar's angular velocity. (b) The radius of the pulsar is estimated to be 10 km. Find the tangential velocity of a point on its equator.

A model train runs on a circular track with radius 1.2 m. Its tangential velocity is 1.2 m/s and it is accelerating with a tangential acceleration of 0.90 m/s2. What is the magnitude of the train’s overall acceleration? Find the angle between the overall acceleration and the centripetal acceleration.

A flywheel has a constant angular acceleration of 0.81 rad/s2. What is its angular velocity 14 s after its angular velocity is 4.8 rad/s?

An LP record rotates at 33 1/3 rpm (revolutions per minute) and is 12.0 inches in diameter. What is the angular velocity in rad/s for a fly sitting on the outer edge of an LP rotating in a clockwise direction?

Explanation / Answer

Given that period is T = 0.033 S

angular velocity is w = 2*pi/T = 2*3.142/0.033 = 190.4 rad/s

radius r = 10 km = 10000 m

tangential velocity is v = r*w = 10000*190.42 = 1.9042*10^6 m/s

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centripetal accelaration is ac = v^2/r

given that v = 1.2 m/s

r = 1.2 m

then a = 1.2*1.2/1.2 = 1.2 m/s^2

atan = 0.9 m/s^2

overall accelaration a = Sqrt(atan^2+ac^2) = Sqrt(0.9^2+1.2^2) = 1.5 m/s^2

required angle is tan(theta) = (atan/ac) = 0.9/1.2 = 0.75

theta = 36.86 degrees

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alpha = -0.81 rad/s^2

t = 14 s

wi = 4.8 rad/s

then use wf = wi + (alpha*t)

wf = 4.8 - (0.81*14) = -6.54 rad/s

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angular velocity is 33 1/3 rev/min = 100/3 rpm

= (100/3)*(2*pi/60) = (100/3)*(2*3.142/60) = 3.5 rad/s

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