A ballerina does a spin. a) Strating from rest, she accelerates to an angular velocity of...

A ballerina does a spin. a) Strating from rest, she accelerates to an angular velocity of 15.7 radians per seconds in 1.2 seconds. she maintains velocity for 1.0 more seconds. How far does she turn in total? Give your answer in number of rotation

b) As she spins she is balanced on an area of her shoe with diameter 3.0cm. Here center of gravvity is located 2.5 feet above the ground and in the equilibrium postion is centered horizontally. How far can she tilt before she will fall over?

Solutions

Expert Solution

w0 = initial angular velocity = 0

= 15.7 rad/s / 1.2 = 13.083 rad/s²

= 0.5 * 13.083 * 2.2*2.2 ( 2.2s = 1.2 s +1.0s)

= 31.66 rad

1 radian (rad) = 0.16 rotations (rot)

= 5.04 rotations

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Q1: Find the final angular velocity if a grinding wheel starts from rest and accelerates at 2...

Q1: Find the final angular velocity if a grinding wheel starts from rest and accelerates at 2 rad/s^2. Q2: If the grinding wheel has a mass of 60kg: a) Find its rotational inertia. b) Find the torque that produces the acceleration. c) Find angular momentum at the instant it has rotated for 8s. I am pretty much lost. Any help will be greatly appreciated.

The wheel of an engine starts to rotate from rest with uniform angular acceleration. It accelerates...

The wheel of an engine starts to rotate from rest with uniform angular acceleration. It accelerates angularly for an unknown time (t1) until reaching an angular velocity of 45.13 rad / s, then maintains that angular velocity constant for 37.8 s. The total angle traveled by the wheel in total is 2398.61 rad. a) What is the angular acceleration with which the wheel began to rotate? b) What is the time (t1) that the wheel was accelerating? c) What is...

An ultracentrifuge accelerates from rest to 90500 rpm in 1.95 min.

An ultracentrifuge accelerates from rest to 90500 rpm in 1.95 min. a. What is its angular acceleration in rad/s2? b. What is the tangential acceleration of a point 9.1 cm from the axis of rotation in m/s2? c. What is the centripetal acceleration in multiples of g of this point at full speed?

A particle accelerates uniformly from rest at 0.15π rad/s2 from rest. The particle’s initial position is...

A particle accelerates uniformly from rest at 0.15π rad/s2 from rest. The particle’s initial position is at 45° from the negative x – axis. If the particle moves a distance 15m along the arc of radius 2m for a time of 1.15 seconds, determine (a) position of the particle after 1.15 seconds from the +x – axis, (b) the initial and final angular velocity, (c) the tangential velocity and acceleration of the particle at 2 seconds?

To visualize the average angular acceleration from a graph of angular velocity: Explain. a) Draw the...

To visualize the average angular acceleration from a graph of angular velocity: Explain. a) Draw the slope as the line connecting two time points (initial and final). b) Draw the slope as a tangent line at a single time point c) Shade in the area between the curve and the x‐axis between two time points

A subway train starts from rest at a station and accelerates at a rate of 2.00...

A subway train starts from rest at a station and accelerates at a rate of 2.00 m/s2 for 14.0 s. It runs at constant speed for 66.0 s and slows down at a rate of 4.00 m/s2 until it stops at the next station. Find the total distance covered.

A flywheel with a radius of 0.390 m starts from rest and accelerates with a constant...

A flywheel with a radius of 0.390 m starts from rest and accelerates with a constant angular acceleration of 0.670 rad/s2. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has turned through 60.0 ∘. Compute the magnitude of the tangential acceleration, the radial...

1. A subway train starts from rest at a station and accelerates at a rate of...

1. A subway train starts from rest at a station and accelerates at a rate of 2.50 m/s ^ 2 for 15.90 seconds. It then runs at a constant speed for 35 seconds and then slows down at a rate of 4.50 m/s ^ 2 until it stops at the next station . (a) What is the speed of the train just before it starts slowing down ? (Ans .: v=39.75 m/s) (b) How long did it take the train...

A flywheel with a radius of 0.400 m starts from rest and accelerates with a constant...

A flywheel with a radius of 0.400 m starts from rest and accelerates with a constant angular acceleration of 0.640 rad/s2. A. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim at the start. Express your answers in meters per second squared separated by commas. B. Compute the magnitude of the tangential acceleration, the radial acceleration, and the resultant acceleration of a point on its rim after it has...

A sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.72...

A sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.72 m/s2. After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is fifty meters long. If the total race is run in 7.85 s, how far does he run during the acceleration phase?

Subjects