An object of mass 1.00kg is moving over a horizontal circular path of radius 2.00m, with a speed of 3.00ms^-1. Determine:
(a) its centripetal acceleration
(b) its kinetic energy
(c) its period
(d) its angular velocity
a: 3.00^2/2.00 = 4.5 ms^-1
b: 0.5 × 1.00 × 2.00^2 × 3.00/2.00^2 =0.5 × 1.00 × 4 × 2.25 = 4.5 J
c: 2 × pi × 2.00/3.00 = 2 × pi × 0.6 = 4/3pi = 4.19s
d: 3.00÷2.00= 1.5ω
on d, the units are radians/sec or 1/sec
Thank you so much!
To solve the given problem, we need to use the formulas related to circular motion. Let's break down the problem and find the solutions.
(a) Centripetal Acceleration:
The formula for centripetal acceleration is given by:
a = v² / r
where a is the centripetal acceleration, v is the velocity, and r is the radius of the circular path.
In this case, the velocity (v) is given as 3.00 m/s and the radius (r) is given as 2.00 m. Plugging in these values, we get:
a = 3.00² / 2.00 = 9.00 / 2.00 = 4.50 m/s²
Therefore, the object's centripetal acceleration is 4.50 m/s².
(b) Kinetic Energy:
The formula for kinetic energy is given by:
KE = 0.5 * m * v²
where KE is the kinetic energy, m is the mass, and v is the velocity.
In this case, the mass (m) is given as 1.00 kg and the velocity (v) is given as 3.00 m/s. Plugging in these values, we get:
KE = 0.5 * 1.00 * 3.00² = 0.5 * 1.00 * 9.00 = 4.50 J
Therefore, the object's kinetic energy is 4.50 J.
(c) Period:
The formula for the period (T) is given by:
T = 2 * π * r / v
where T is the period, π is a mathematical constant approximately equal to 3.14, r is the radius, and v is the velocity.
In this case, the radius (r) is given as 2.00 m and the velocity (v) is given as 3.00 m/s. Plugging in these values, we get:
T = 2 * 3.14 * 2.00 / 3.00 = 4.19 s (rounded to two decimal places)
Therefore, the object's period is approximately 4.19 s.
(d) Angular Velocity:
The formula for angular velocity (ω) is given by:
ω = v / r
where ω is the angular velocity, v is the velocity, and r is the radius.
In this case, the velocity (v) is given as 3.00 m/s and the radius (r) is given as 2.00 m. Plugging in these values, we get:
ω = 3.00 / 2.00 = 1.50 rad/s
Therefore, the object's angular velocity is 1.50 rad/s.